# GNSS-R Observations of Marine Plastic Litter in a Water Flume: An Experimental Study
## 3 Results  
A total of 123 potentially valid data files have been analyzed. As explained before, the high carrier-to-noise ratio (CN0) allows for the use of a coherent integration time as short as T\({}_{\rm coh}\) = 1 ms, without any incoherent averaging (N\({}_{\rm inc}\) = 1), which means that GNSS-R signals at 1 ms sampling rate could be analyzed. During the experiments, the relative calibration between the reflected and the direct signals was first performed using the calm water as a reference (i.e., the known reflection coefficient at LHCP and RHCP for a given frequency, incidence angle, water temperature and salinity). Since the measured changes were very small, a differential analysis was conducted. In some occasions, the reference observation was not directly acquired immediately before, or even if it was, the surrounding conditions were not exactly the same (e.g., variable multipath as people moved around). This translated into fluctuations of the direct signal that were used to monitor the data quality. There are other examples where radio frequency interference (RFI) was very obvious, and these measurements had to be discarded as well. Some of the problems encountered include multipath in the direct signal (up-looking antenna) as well as RFI in the reflected signals (down-looking antennas), or fast electromagnetic interference (EMI with a period of T = 20 ms, \(f\) = 50 Hz) probably from power lines, although of very small amplitude (\(\sim\)0.04 dBPp), which can be neglected for all purposes (Figure 7). A second ripple of period T = 0.1 s (i.e., 10 Hz) with an amplitude of \(\sim\)0.1 dBPp is also noticed, which seemed to be linked to small waves propagating in the water surface despite the fact that the mechanical pedals had been turned off for a while. This is normal, as for a very large basin like the Atlantic Basin, it is not possible to have a perfectly flat surface. Bad quality or corrupted data were discarded. The minimum detectable changes in Figure 7 set the limit of the smallest signature that can be detected (\(\sim\)0.04 dB). The analysis performed for each scenario includes (e.g., Figure 8 for clean rough water surface without capillary waves):  
* For the amplitude (power): (a) time series, (b) multi-path quality check: scatter plot of received power at left (RL) and right (RR) polarizations in dB full scale (dBFs) versus the direct signal power also in dBFs, (c) spectra, (d) histogram of the received power at RL and RR polarizations;
* For the phase: (e) time series, (f) scatter plot of the phases at RR versus RL polarizations, (g) spectra, (h) histogram of the received phases at RL and RR polarizations. Statistical descriptors are the mean, the standard deviation (\(\sigma\)), the kurtosis (k), and the skewness (sk). Recall that the RL polarization is defined as incident wave at RHCP, and the reflected one at LHCP, and RR polarization as defined as incident wave at RHCP, and the reflected one at RHCP. Time series (Figure 8a,e plots) allow for the gathering of an insight of the power or phase variations, which are very noticeable in the cases when the water surface is roughened. Also, the shape is different depending on the spectrum (i.e., sinusoidal vs. JONSWAP). While for a flat surface the received power is nearly constant and the phase has a Gaussian distribution, as it is just noise (not shown), for a roughened water surface, the received signal has a particular amplitude (Figure 8d) and phase (Figure 8h) distributions. The spectral analysis (e.g., Figure 8c) reveals a peak at the dominant wave period (e.g., \(\sim\)0.86 s, or \(\sim\)1.2-1.3 s in most cases), as shown in Figure 5. Peaks in the spectrum above \(\sim\)10-20 Hz cannot be attributed to capillary waves, and they can only be attributed to electromagnetic interference. The same behavior occurs for the phase.