Evaluation of Ku-band Ground-based Interferometric Radar Using Gamma Portable Radar Interferometer

Abstract

The Gamma Portable Radar Interferometer (GPRI) is a ground-based real aperture radar (RAR) that can acquire images with high spatial and temporal resolution. The GPRI ground-based radar used in this study composes three antennas with a Ku-band frequency of 17.1-17.3 GHz (1.73-1.75 cm of wavelength). It can measure displacement over time with millimeter-scale precision. It is also possible to adjust the observation mode by arranging the transmitting and receiving antennas for various applications: i) obtaining differential interferograms through the application of interferometric techniques, ii) generation of digital elevation models and iii) acquisition of full polarimetric data. We introduced the hardware configuration of the GPRI ground-based radar, image acquisition, and characteristics of the collected radar images. The interferometric phase difference has been evaluated to apply the multi-temporal interferometric SAR application (MT-InSAR) using the first observation campaigns at Pusan National University in Geumjeong-gu, Busan.

1. Introduction

Satellite radar interferometry is a widely used technique for measuring displacement caused by landslides, earthquakes, volcanoes, and land subsidence (Cabral-Cano et al., 2008; Colesanti and Wasowski, 2006; Massonnet et al., 1993; Moreira et al., 2013; Park and Hong, 2021). However, satellites that travel along a fixed polar orbit should have a relatively long revisit cycle, which results in lower temporal resolution and limitations in obtaining timely observations of the study area. Additionally, when very precise displacement measurement is needed, it may be challenging to acquire coherent interferometric radar images with sufficient spatiotemporal resolution or precision (Werner et al., 2008a).

The Gamma Portable Radar Interferometer (GPRI) is a Ku-band ground-based real aperture radar (RAR) designed to move easily and install quickly. Thus, it is possible to measure deformation by selecting an appropriate imaging geometry by adjusting various angles of incidence and rotation, reducing the coverage loss in the observation area. Additionally, it can obtain multi-temporal images with short time intervals for high temporal resolution, which enables the measurement of continuous fast-moving deformations such as glacial movement and landslides. The ground-based radar can also be utilized to calibrate and validate existing radar systems, such as satellites and aircraft, and to evaluate the feasibility of new concepts of radar techniques(Kos et al., 2013; Lee et al., 2007; Riesen et al., 2011). The ground-based radar is highly applicable for estimating deformation with a precision of millimeter-scale and can be used for multiple purposes such as evaluating the stability of infrastructures like bridges or dams, measuring the displacement of slopes, monitoring long-term surface displacement, and estimating land subsidence rate (Caduff et al., 2015). Over the past few years, the usage of ground-based radar has been steadily developing, including assessing structural stability (Werner et al., 2012), evaluating landslide and rock slope instability (Kos et al., 2013; Leva et al., 2003;Tarchi et al., 2003), observing glacial ice surface movement based on Ku-band ground radar (Riesen et al., 2011; Voytenko et al., 2012; Wiesmann et al., 2014), and monitoring time-series land subsidence (Werner et al., 2016). Astudy on rock slope displacement measurement using both ground-based radar and satellite imaging radar has also been conducted (Strozzi et al., 2015). A few kinds of research on ground-based radar have also been reported in Korea. Studies have been conducted on the development of C-band ground-based synthetic aperture radar (GB-SAR) systems (Lee et al., 2007) and the implementation of X-band automobile-based SAR systems (Cho et al., 2006).

In this paper, the hardware composition and the characteristics of the GPRI ground-based radar are introduced, and the preliminary acquisition results using various observation modes and interferometric feasibility for time-series displacement maps are presented.

2. Gamma Portable Radar Interferometer

2.1. Characteristics and Principles of the GPRI

The GPRI is a Ku-band frequency-modulated continuous-wave (FMCW) radar. The FMCW radar generates and emits a continuous wave of signal, and the frequency of the transmitted wave changes linearly with time. Fig. 1 is a schematic diagram demonstrating the relationship between the transmitted FMCW chirp and the received echo.Asingle transmitted chirp starts at a time T₀ and lasts for time T (sec).

B = | f₁ – f₀ |       (1)

Fig. 1. Transmitted frequency-modulated continuous-wave (FMCW) chirp and received echo. Modified from Werner et al. (2008a).

Bandwidth, B, is the difference between the starting frequency f₀ and ending frequency f₁, and the values commonly used in GPRI are f₀ = 17.1 GHz and f₁ = 17.3 GHz.

\(\begin{aligned}\delta_{r}=\frac{c}{2 B}\end{aligned}\)       (2)

Chirp bandwidth is directly translated into the slant range resolution of the radar. The range resolution, δ_r, is established by the bandwidth B and the speed of light c.

\(\begin{aligned}\tau=\frac{2 r}{c}\end{aligned}\)       (3)

The echo reflected from a single scatterer is delayed by a time τ and then returns. τ representsthe propagation time delay, where r is the distance of the target, and c is the speed of light. The propagation time delay τ leads to the offset, f_b, between the transmitted signal and the received signal and the distance of the object is determined by measuring the frequency difference between the transmitted signal and the received signal from the scatterer. Because the FMCW radar receives the echo simultaneously while transmitting, the instrument should have separate transmitting and receiving antennas.

The GPRI has 2-meter long real-aperture antennas and consists of one transmitter antenna and two receiver antennas. It has a range resolution of approximately 75 cm and an azimuth resolution of approximately 6.72 m at a 1 km distance with line of sight (LOS) direction. The measurement accuracy is approximately 1 mm at 1 km, allowing for precise phase acquisition for interferometric applications (Werner et al., 2008b). The GPRI composes a total of six antennas with three vertical polarization (V-pol) antennas and three horizontal polarization (H-pol) antennas. These antenna compositions enable the acquisition of full-polarization images of HH, HV, VV, and VH through the simultaneous installation of all V-pol and H-pol antennas.

Table 1. Characteristics of the Ku-band Gamma Portable Radar Interferometer (GPRI)

The GPRI real-aperture imaging system acquires images line-by-line as the antenna rotates with respect to the central axis. This RAR system is designed to minimize interferometric coherence degradation during image acquisition which might be occurred in SAR systems. Once a change occurs in the target area during the acquisition of the SAR image, the degraded coherence of the observation area could be reflected in the radar echoes in the SAR image. The real-aperture image acquisition system only needs to keep the object in a fixed state for a millisecond transmission time, allowing it to measure the deformation of a region that includes both fixed and low-coherence scatterers.

2.2. Interferometric Mode

Radar interferometry is a method of generating topographic height or measuring displacement by calculating the phase difference between two radar images obtained over the same area (Rosen et al., 2000).

\(\begin{aligned}\varphi_{i}=-\frac{4 \pi R_{i}}{\lambda}+\varphi_{c}\end{aligned}\)       (4)

In a complex radar image, the phase backscattered from a single scatterer is represented by φ_i and the unit of phase isradian (rad). The phase value is proportional to the slant range distance, R_i , and φ_c is a fixed phase offset value generated from radar electronics and signal processing, etc.

Δφ = φ₁ – φ₂ = Δφ_disp +Δφ_topo +Δφ_atm +Δφ_scatter +Δφ_process +Δφ_err       (5)

The phase calculated by applying the interferometric technique to the two radar images includes various phase components. Δφ represents the phase difference between the two images calculated in an interferogram. Δφ_disp is the phase difference due to surface displacement, Δφ_topo is the phase contribution from topographic height, Δφ_atm is the time delay phase error due to atmospheric artifacts, Δφ_scatter is the phase error depending on the scattering characteristics and roughness of the surface, Δφ_process is the error occurring during the data processing, and Δφ_err is the other general error. To extract phase information by surface displacement, phase components due to topography and other unnecessary phase information can be removed by applying the differential interferometric method. Differential interferograms can be generated by applying this technique to time-series images acquired with the same receiving antenna of the ground-based radar through repetitive image measurements at a precisely fixed position. The geometric baseline between the consecutive radar image pairs should be zero. Thus, the topographic phase contribution is not included in the interferogram, and the differential interferogram can be constructed immediately without additional processing to remove the topographic phase.

\(\begin{aligned}\delta_{\text {los }}=-\frac{\lambda \varphi}{4 \pi}\end{aligned}\)       (6)

The GPRI measures the displacement in the LOS direction. Given a differential phase difference φ, the LOS displacement is expressed as δ_los. To measure high-precision of displacement, it is essential to install the center of the antenna facing the region of interest parallel to the direction of change of the object. If the surface deformation is mainly vertical, a relatively steep look angle is considered, which allows for the acquisition of images with a sufficient spatial resolution (Werner et al., 2016). Since the radar measurement is for the round-trip of the 2-way path, a 2π phase change of the scatterer in the interferogram corresponds to a displacement of 8.72 mm in the GPRI. It is very important to minimize the position error which might be generated during the re-installation for repeated experiments to within 1 cm.

2.3. Digital Elevation Model Generation Mode

Interferograms for the generation of digital elevation models (DEMs) can be produced by using images acquired simultaneously from both independent receiving antenna channels. By adjusting the position of the transmitting and receiving antennas, vertical geometric baselines may vary from 25 to 60 cm. In the case of the GPRI, when three antennas are installed in the antenna tower, the antenna located in the middle of the tower is spaced 35 cm apart from the antenna at the top and 25 cm apart from the antenna at the bottom. Therefore, the two independent receiving antennas may have vertical baselines of 25 cm, 35 cm, and 60 cm, and the maximum vertical baseline can be obtained if the receiving antennas are placed at the top and bottom. Since the GPRI acquires images at very short time intervals of less than 20ms, the interferogram generated by the two images from each receiving antenna does not suffer from temporal decorrelation (Werner et al., 2012). After the generation of the interferogram using the images taken at the same time, the DEM can be finally acquired through the phase unwrapping, geocoding, and DEM height conversion (Strozzi et al., 2011; Werner et al., 2008a).

3. Data and Methods

3.1. Data

The Pusan National University campus area located at Geumjeong-gu, Busan, was selected as a study area to conduct experiments on the GPRI ground-based observation. Twice experiments were conducted, and in the first experiment, a total of 20 images were acquired for 40 minutes at 2-minute intervals. In the second experiment, we obtained five images for 10 minutes at 2-minute intervals. The transmitting antenna was placed at the top, and the two receiving antennas were placed at the bottom in turn. The vertical baseline between the transmitting antenna and the two receiving antennas was 35 cm and 60 cm, respectively. The first experiment on Oct. 14, 2022, used a single polarization configuration with three vertical antennas. In the second experiment conducted on Oct. 19, 2022, the GPRI experiment was performed in full-polarization mode using both three V-pol and H-pol antennas, and we compared the amplitude images of each polarization.

Table 2. Descriptions of data used in this study

Fig. 4 is an example of the raw data signal from the second receiving (RX2) antenna obtained at 16:51:00 on Oct. 14, 2022. The upper graph shows the signal of the raw data as a function of time, and the lower graph represents the range-compressed signal as a function of distance in the range direction. The raw data graph of each receiving antenna can be generated by a console and checked the raw data quality immediately after image acquisition, and suitable parameters can be selected according to the characteristics of the study area by evaluation of the signal quality.

Fig. 2. The Gamma Portable Radar Interferometer (GPRI) Ku-band ground-based radar installation.

Fig. 3. Map of the study area. The red arc is the acquisition range (Source: Google Earth).

Fig. 4. Raw data plot of second receiving (RX2) antenna.

3.2. Methods

Data processing was performed using commercial software of GAMMA to produce coherence and interferogram by applying the interferometric technique to the images obtained in the GPRI experiment. Multiple interferograms were generated, and the phase statistics of the 10-minute interval interferograms were calculated to examine whether a stable phase value was maintained during the GPRI experiment. Then, we divided the interferometric image into building and forest areas by specified polygons based on prior knowledge of the study area and selected fifty pointsrandomly from each area to estimate the phase stability. The selected points should have identical image coordinates for subsequent statistical analysis. Statistical analysis, such as the average and standard deviation of the calculated interferogram, was applied.

Since the Ku-band ground-based radar used in this study acquired images from the same position and using the same antenna, the topographic phase removal from the initial interferogramwasn’trequired. However, correction of atmospheric effects during microwave propagation was still necessary due to the sensitivity of the Ku-band’sshort wavelength to water vapor (Lee et al., 2010; Luzi et al., 2004). We performed the process of removing atmospheric effects in the interferograms. The atmospheric phase variation in the differential interferograms appeared as a linear residual phase ramp that became more noticeable as the temporal baseline between the two image pairs increased. To reduce the atmospheric effects, we modeled the linear phase variation caused by atmospheric effects in unwrapped differential interferograms using a polynomial and subtracted the estimated atmospheric phase from the initial differential interferograms. Then we compared the phase statistics before and after atmospheric correction.

We also analyzed the effect of temporal baseline in coherence over time. The first image acquired in the experiment on Oct. 14, 2022, was used as a reference image, and a total of 19 interferometric coherence images were produced with consecutive images acquired at 2-minute intervals. The coherence values were extracted from50 randomly selected points for each image, and the decorrelation in coherence over time was analyzed by averaging the coherence values for each image.

4. Results

4.1. Interferogram Analysis

Fig. 5 is the multi-looked intensity (MLI) image, and the intensity image can show the high spatial resolution of the study area. We noticed that large shadow topographic effect, which results from the large incidence angle between the radar and the object. Shadow effect ismainly detected in tall mountain areas, however, it can also appear in the vicinity of tall buildings.

Fig. 5. The multi-looked intensity (MLI) image acquired on Oct. 14, 2022, on a Google Earth map. The red and blue polygons represent the building and mountain areas used for statistical analysis in this study, respectively.

A differential interferogram was obtained from an interferometric pair with 10-minute intervals in the first experiment, as shown in Fig. 6.The interferogram was generated using two images acquired with the same RX2 antenna. Since topographic phase removal was not necessary in this case, the differential interferogram was obtained immediately. Statistical analysis of the interferometric phases with the 10-minute temporal baseline shows that the average is 0.15 rad (~0.21 mm), and the standard deviation is 0.29 rad (~0.40 mm) in the building area. The average is –0.12 rad (~–0.17 mm), and the standard deviation is 1.66 rad (~2.30mm) in the forest area. After atmospheric phase removal, the statistics of the 10-minute interval differential interferogram were obtained, with an average of –0.03 rad (~–0.04 mm) and a standard deviation of 0.29 rad (~0.40 mm) in the building area and an average of –0.27 rad (~–0.37 mm), and a standard deviation of 1.69 rad (~2.35 mm) in the forest area. The average of both areas has been slightly improved though the standard deviation is not varied much. These results imply that atmospheric phase removal is essential even in the only 10-minute temporal baseline.

Fig. 6. Differential interferometric phase overlayed with backscatter intensity image.

Fig. 7 represents the distribution of phase values of 50 points in the building and forest area randomly selected to obtain phase statistics from the differential interferogram at 10-minute intervals in Fig. 6. Fig. 7a shows the phase distribution of the initial differential interferogram, while Fig. 7b shows the phase distribution after atmospheric phase removal. As a result of comparing the two statistics and distribution, we confirmed that the phase distribution corresponds to the previous analysis results. The average is calculated to be very close to zero in the building area, and the average value is improved by –0.15 rad after atmospheric phase removal in the forest. There is no significant difference in standard deviation values for both buildings and forests.

Fig. 7. Comparison of phase distribution for 10-minute interval interferograms before and after atmospheric correction. (a) Phase distribution of each 50 points in the differential interferogram. (b) Phase distribution of each 50 points in differential interferogram after atmospheric phase removal.

We plotted the variations in the interferometric phase according to the increase in the temporal baseline for the building and forest area in a total of 19 differential interferograms (Fig. 8). The average of phases randomly selected 50 points in both building and forest area was used as a representative value of each image.The entire experiment has been conducted over a relatively short time period (a maximum temporal baseline of 38 minutes). Thus, there was no significant surface displacement in the study area with a very short temporal baseline. As a result, we could expect uncorrelated phase results with respect to the temporal baseline after atmospheric correction. In particular, the phase change over time is expected to be close to zero for stable scatterers like buildings. Therefore, little residual phase ramp should be observed after atmospheric correction. While the initial interferometric phase represents an upward trend, the after atmospheric correction significantly reduced the phase artifacts trend in the building area (Fig. 8a). In the forest area, there was a slight phase difference after the removal of the atmospheric effect, however, no distinct pattern was evident before or after correction. We also compared phase statistics between the initial differential interferograms and the differential interferograms after atmospheric phase removal for each area. The average of phase values in the building area is 0.58 rad (~0.80 mm), and the standard deviation is 0.38 rad (~0.53 mm).After atmospheric phase removal, the average is 0.11 rad (~0.15 mm), and the standard deviation is 0.13 rad (~0.18 mm) in the building area. In the forest area, the average is 0.04 rad (~0.06 mm), and the standard deviation is 0.25 rad (~0.35 mm). After removing the atmospheric phase, the average is –0.05 rad (~–0.07 mm), and the standard deviation is 0.24 rad (~0.33 mm). The average and standard deviation of the phase values in the building area are greatly reduced after the atmospheric phase removal. In the forest area, the average decreased after removing the atmospheric phase, but there was no significant difference in standard deviation. The refinement of tendency and phase statistics in the building area suggests that atmospheric correction should be applied in the very short Ku-band microwave signal processing.

Fig. 8. Comparisons of phase values in each of the 19 differential interferograms before and after atmospheric correction in (a) the building area and (b) the forest area.

The topographic interferogram was produced from images obtained with DEM acquisition mode using two receiving antennas on Oct. 14, 2022 (Fig. 9). Unlike the differential interferograms, interferometric phases reflected the topographic height that could be seen. Each fringe indicates the path difference related to topography, however, additional processes are required for the final production of the DEM.

Fig. 9. Spatial interferogram phase (Baseline=25 cm).

4.2. Coherence Analysis

Fig. 10 shows coherence between two images obtained at 10-minute intervals. High coherence (> 0.9) is maintained in buildings, but low coherence values appear in the forest area.

Fig. 10. Interferometric correlation coefficient overlaid with backscatter intensity image.

As a result of the temporal decorrelation of the two areas obtained on Oct. 14, 2022, it is confirmed that the coherence value is 0.9 or higher in the building area, and in the case of forests, the coherence value is about 0.5. The standard deviation is 0.01 in the building and 0.02 in the forest. The comparison between the two values indicates a lower standard deviation in the building, though both standard deviations are quite low. The tendency of decreasing the coherence values in the building over a total of 40 minutes of experimental time is observed, and in the case of forests, no tendency is observed due to the increase of the temporal baseline.

Fig. 11. Temporal decorrelation of building and forest area.

4.3. Full-polarization Observation

Fig. 12 shows examples of Ku-band ground-based radar polarimetric acquisition mode. Fig. 12a-d are the HH, HV, VH, and VV amplitude images of the study area, respectively. It can be observed that in areas with high volume scattering, such as forests, HV and VH images exhibit higher values, while in areas with high double-bounce scattering, such as buildings, HH, and VV images show higher values. The linear signals observed in Fig. 12a, d are likely the result of saturation caused by surrounding structures during the experiment.

Fig. 12. Examples of Ku-band ground-based radar polarimetry. (a)-(d) show the HH, HV, VH, and VV amplitude images of the study area.​​​​​​​

5. Conclusions

This study presents the characteristics and various observation modes ofthe GPRI Ku-band ground-based radar and provides the preliminary results of two experiments fulfilled in Geumjeong-gu, Busan. The study demonstrates the application of radar interferometry to the acquired images to produce coherence maps and interferograms and how precise phase values can be obtained through the GPRI observation for various temporal baselines. The statistical analysis of the interferometric phases obtained from a differential interferogram with a 10-minute interval indicates that maintenance of stable phase values is possible. In addition, it highlights the importance of correcting for the atmospheric effect of the Ku-band ground-based radar on interferograms and the requirement to maintain accurate positional accuracy with a positional error of less than 1 cm during equipment re-installation for repeated multi-temporal observations for long periods. The results of the GPRI experiment demonstrate the high availability of the Ku-band ground radar for various observation modes, including displacement detection, DEM mode observation, and acquisition of full-polarization data. Further studies, such as long-term surface displacement observation and scattering characteristics analysis through the application of radar interferometry and observation modes of the Ku-band ground radar, will be conducted.