The results shown in this paper are based on several measurement campaigns in which an ad hoc receiver based on a software-defined radio solution was used. This system was basically composed of an antenna, a plastic-wood support where the receiving antenna was fixed in order to maintain a specific height from the terrain, a radio frequency front end circuit for the frequency down-conversion of the received signal and for its digital conversion, and a suitable hardware device to store and process the data (see Figure 1).
3.1 Hardware
A summary of GPS system characteristics can be found in [36]. Each GPS satellite broadcasts a carrier signal at 1,575.42 MHz, referred to as ‘L1,’ modulated by a civilian code (the so-called Coarse Acquisition code). Additionally, another code is broadcasted through a carrier frequency of 1.2276 GHz (L2) for military use, but reception of this signal requires complicated signal processing since it is encrypted. Even if at the time of the experiment few satellites started the transmission of the new civilian L2C signal, all the algorithms were based on the processing of the Coarse Acquisition (C/A) code. Therefore, only the GPS L1 carrier signals were used in our bistatic radar remote sensing experiment. The signals are encoded with timing and navigation information and transmitted with right-hand circular polarization (RH). The receiver can then calculate the positions of the transmitting satellites and use this information to calculate its own position and GPS time. A low-gain, quasi-hemispherical, zenith patch antenna is normally used to receive the direct signals. The GPS signals are also reflected off by the Earth's surface and can be received by a nadir-viewing antenna at a further delay with respect to the direct signal. After reflection, the scattered signal is predominantly LH for typical incidence far away from the Brewster angle. A low-gain, quasi-hemispherical, LH nadir antenna was used to measure the scattered signal. This antenna was chosen in order to have more flexibility in the measurements of signals characterized by different angles of incidence and because the geometry slowly changes with transmitter and receiver positions. Even if the cross-pol level of our antenna was not very good (approximately -15 dB), the RH component of the reflected signals (generated by scattering phenomena inside the glistening zone) is expected to be from -10 to -20 dB lower than the LH one. This means that the contribution due to the RH power available at the output of the LH antenna is a very small (and negligible) fraction of the wanted LH component. Other important figures of merit to be considered for the choice of the antenna are the half-power beamwidth (HPBW; and its projection on the ground, i.e., the antenna footprint) and the entire antenna's radiation pattern. The HPBW should be as wide as possible, in order to be able to contemporaneously acquire as many reflected signals as possible. The signals can then be easily separated on the base of the Pseudo Random Noise (PRN) code modulating the GPS L1 frequency (called C/A code), which uniquely characterizes the transmitted signal.
It has to be noted that only a portion of the footprint will be ‘sensitive’ to the reflected signal, namely the first Fresnel zone, which is the projection on the ground of the first Fresnel ellipsoid defined considering the geometry and the wavelength [37]. The majority of the reflected power is generated within this area, particularly when the terrain can be considered flat at the used wavelength. If scattering over a rough surface occurs, a wider area (the so-called glistening zone) should be taken into account.
Even though the antenna allows simultaneous reception of both the polarized components of the reflected signal, only the LH one was processed in these experiments. The processing of the RH component can provide some interesting contribution to minimize surface roughness effects when the goal is to remotely sense some geophysical parameter of the surface. The hypothesis that for moderately rough surface the ratio of two orthogonal polarizations does not depend on the surface roughness was formulated by [38]. Recently, the fact that both reflection coefficients for reflected LH and RH are sensitive to surface roughness but their ratio is seen to be independent from the roughness was experimentally proved by [23].
In our case, the goal was to detect objects with some metallic part, just under the ground surface. In this situation, the signal received after the scattering from the metallic part is strong enough to be detected even if the object is placed under a very rough surface.
Another important hardware choice concerns the radio frequency front end circuit. The SiGe GN3S Sampler v2, developed from the Colorado Center for Astrodynamics Research, was used [39]. It is composed of two main integrated circuits. The first one is an application-specific integrated circuit (ASIC), which basically amplifies the incoming radio frequency (on the L1 GPS bandwidth), filters it, down-converts it from the GPS carrier frequency to an intermediate frequency of 38.4 MHz, and samples it (with a sampling rate 8.1838 MHz, which can provide up to eight samples per code chip of the modulating C/A code). Two bits for representing both the in-phase and the quadra-phase samples of the signal component are used and are sent to the second circuit, the microcontroller, which transfers in real time the ASIC-generated samples into a USB.
Basically, the system we developed is a software-defined radio device. Even if the other steps of signal processing are performed following a pure software approach, a device to store and to post-process all the samples of the raw signal available is necessary. In this case, we developed two different solutions. The first one is based on the use of a laptop PC which is directly connected to the front end through the USB port (see Figure 2, left). This configuration can be easily extended to support two different front ends, one of them connected to an up-looking RH antenna, in order to allow the collection also of the direct GPS signals for positioning purposes and for georeferencing specular reflection points into the terrain. The direct signal can also be used for calibration purposes. This is an important task to be performed if the goal is to quantitatively extract geophysical parameters from the reflected signal or to have an idea on the Doppler shift characterizing the reflected signal. Also in this case, a software GPS receiver solution can be easily adopted, implementing all the standard closed-loop signal processing steps to the digital samples of the received raw signal (see for example the NGene software receiver, developed by the NAVigation Signal Analysis and Simulation (NAVSAS) group of the Politecnico di Torino, Italy [40]).
A more stand-alone, compact, and trendy solution was based on a system on chip (SoC) device able to store a large amount of raw samples available during a single measurement: the Hackberry A10 Development Board [41], (see details of this board in Figure 3). The entire system was implemented on an electronic board (100 mm × 80 mm). Thanks to its lightness, small dimensions, and independency from external power source, it can be easily used as a payload for a small unmanned aerial system (UAS), remotely and/or automatically controlled. Some internal subsystems - including the storage device, the oscillator, the power supply (it can be powered thanks to an external battery which is also able to provide the required current to the antenna's low-noise amplifier), the Ethernet LAN, and the USB management - were customized in order to better suit the performance of the front end. A customized version of the operating system based on Linux Debian to be installed on the Hackberry board processor was also developed. The entire device was able to operate via the SSH protocol using either the Ethernet LAN port or a wireless connection (an internal Wi-Fi transmitter is available). This is extremely useful in order to access the onboard firmware which contains several user setup parameters.The board, the front end, and the antenna were finally integrated into a single box, as shown in Figure 2, right. This second solution was adopted from static position only in order to test its effectiveness. After the board is switched on, the operating system boot takes around 80 s. Data can be acquired for a certain user-defined time interval (around 40 s) or up to when the onboard RAM is full. The data acquired are automatically downloaded into an onboard SD card. The performances of the Hackberry A10 Development Board are not adequate for the processing steps explained in ‘Section 3.2’; acquired data are currently post-processed by a standard PC.
3.2 Signal processing and post-processing software
Data stored on the PC or on the SD card were post-processed implementing the first signal processing stages for standard open-loop GPS data acquisition using ad hoc MATLAB routines. The open-loop approach was implemented in order to avoid time delays due to the first fix standard procedures and to avoid possible signal loss of lock due to low SNR values [42]. For each available satellite, a software routine dispreads the reflected signal reconstructed from its in-phase and quadra-phase intermediate frequency components. Basically, this standard operation consists in correlating raw data with a replica of the transmitted GPS C/A code locally generated by a software routine, in both delay and Doppler frequency shift domains (see for example [36] for a more detailed discussion of basic GPS signal acquisition and tracking). For each Doppler shift (analyzed with a resolution of 1 kHz or 10 Hz in a bandwidth of 20 kHz or 200 Hz around the carrier frequency for the first raw solution or for the more refined one), the correlation was performed in the frequency domain instead of doing it in the more time-consuming time domain. The correlation amplitude is then squared in order to get the correlation power (Figure 4 shows an example). This variable is provided for the entire duration of one GPS C/A code period (1 ms) with a time resolution provided by the sampling rate of the radio frequency front end (which is 8.1838 MHz, i.e., 0.125 C/A code chip length being the entire code formed by 1,024 chips). This time interval is also known as coherent integration time. In order to improve the SNR, in principle, it is possible to coherently integrate this value considering 20 ms of data. Longer intervals require knowledge of the navigation data bit hidden in the C/A code sequence. From the delay Doppler map (DDM), the so-called delay waveform (DW; the entire correlation function containing the maximum value evaluated in function of the range) was extracted. Since the reflected signal power is attenuated by the surface scattering process [13], the correlation peak of the reflected signal hardly emerges. Therefore, before extracting DW, a noncoherent integration was performed summing together several consecutive DDMs. The impact of different noncoherent integration time intervals was analyzed in detail, and finally, a 500-ms interval was chosen for processing all the acquired data sets. Further increase of the integration time does not change significantly the final results. Moreover, the integration time cannot be increased too much in applications where the receiver is moving. An example of an integrated DDM is shown in Figure 5, left. There are 8,184 samples in the x-axis (one C/A code period) and 20 frequency steps within the range from -10 to 10 kHz (1-kHz step, y-axis). The z-axis shows the normalized correlation power. The corresponding DW is shown in Figure 5, right.
A noncoherently integrated peak value is therefore available each 500 ms. Corresponding SNR time series can therefore be estimated. The SNR of the received signal can be written as
(1)
where PS and PN are the signal and noise power before despreading, respectively. Ambiguity functions Λ and S represent the ‘attenuation’ due to power correlation misalignments, in delay and frequency, and G
D
is the so-called processing gain (approximately 30 dB) due to the despreading of the GPS C/A code. P
N
is the input noise power that can be expressed as
where k is the Boltzmann constant, k = 1.380 × 10-23 J/K; TN is the estimate of the receiver noise equivalent temperature (which can be approximated as TN = (NF - 1) 290), NF (dB) being the receiver noise figure (it can be estimated in the range of 1.0 to 2.5 dB); and B
w
= 1/TI is the signal bandwidth determined by the coherent integration time TI (1 ms in our case). It results in PN = - 176.3 dB W. The antenna's temperature (TA) was not taken into account in the input noise power evaluation because the measurements were carried out to detect the metallic object and to estimate its dimension by evaluating the relative increase (or decrease) of the SNR, without changing the experimental setup.
The SNR to be estimated is related to the correlation peak available after despreading. Thus, the attenuation factor due to the ambiguity function is close to 1 (the reflected signal is received with a delay and Doppler shift ). Finally, the received signal power PS can be expressed by the following simplified equation derived from Equation 1:
(3)
where Φpeak is the absolute signal to noise ratio (ratio between the pure signal and the noise powers) and it can be easily evaluated considering the normalized DW. In particular, the noise floor can be estimated as the DW averaged level computed over a region of delays where no signal Φpeak is present. Therefore, the SNR obtained by the measurement can be easily derived as follows:
(4)
The estimated total received power PS (coherent signal power) can be derived from Equation 3. Even if only the value of the correlation peak was used to estimate SNR, this open-loop approach allowed us to develop and implement the software procedure to evaluate the entire autocorrelation function, whose knowledge could be used in the future for other GNSS-R applications, more oriented to the remote sensing of surface parameters. As far as the detection of buried objects is concerned, the estimation of the SNR time series is enough, as it will be discussed in ‘Section 5.’