**4. Results**

The signals from five different satellites, including four MEOs and an IGSO, were used for computing reflector heights at different periods. The SSHs were separately derived, based on B2a and B1C signals from 13:30 to 22:00 on 5 November (local time). In general, continuous GNSS-R altimetry solutions were achieved for more than eight hours. As the reflector heights could be derived by using the code-level path delay measurements of one satellite, we selected signals from only one satellite over a certain period of time. The sea

surface was smooth in general during the experiment, so the path delay measurements were derived from the peak point positions of the direct and reflected waveforms. As the coherence time for both B1C and B2a codes was 10 milliseconds, each time slot of 10 milliseconds produced an estimate of the path delay. Considering that our SDR runs very slow, we computed a delay measurement every 50 milliseconds to save time. So, there are 21 delays in one second, and their median value was chosen for altimetry retrievals. Figures 4 and 5 show SSHs derived from B1C and B2a code-level delay measurements, respectively. We find that the solutions of both B1C and B2a can reflect the trend of the sea surface change, compared with the measurements of the radar altimeter. However, the noise level of B2a is larger than that of B1C. It should be noted that the gaps around 14:10 in Figures 4 and 5 were caused by an accidental interruption in the power supply at the beginning of our experiment.

**Figure 4.** SSHs derived from B1C code-level delay and radar altimeter measurements for more than eight hours.

**Figure 5.** SSHs derived from B2a code-level delay and radar altimeter measurements for more than eight hours.

In order to evaluate the precision of GNSS-R altimetry based on the two kinds of new BDS civil codes, we differentiated between the solutions and radar altimeter measurements. Figures 6 and 7, respectively, show their height difference sequence with the satellite elevation angles for B1C and B2a signals. The root mean square (RMS) values of the two sequences are 0.394 m and 0.668 m for B1C and B2a, which are better than the solutions derived from GPS C/A and BDS B1I code [20]. It is worth noting that the divergence is a minimum of between 60◦ and 70◦ in both the cases. This is because the signals with elevation angles around 60◦ have small incidence angles for both upward- and downwardlooking antennas, thanks to their 30◦ tilted angles. The gain of antennas is maximal in these directions, indicating that higher gain of antenna will help improve the precision of the

solutions. On the other hand, both the direct and reflected signals with higher elevations have higher power, so that the divergence is a minimum of around 65◦ instead of 60◦.

**Figure 6.** Differences between measured SSHs using monostatic radar and B1C signals at different elevations.

**Figure 7.** Differences between measured SSHs using monostatic radar and B2a signals at different elevations.

The above analysis shows that the precision of GNSS-R code-delay altimetry achieved from B1C is better than that from B2a. In this study, the coherent time is 10 milliseconds for both signals. The code rate of B2a signals is 10 times that of B1C, but the complicated code construction of B1C produces its wider bandwidth compared to B2a. In addition, the results of a positioning experiment using BDS-3 signals showed that B2a signals have relatively poor quality, although they have stronger power than the other open available ranging code [21]. Affected by the above factors, GNSS-R code-delay altimetry based on B2a signals from our experiment has worse precision than that based on B1C signals.

Since our altimetry solutions are derived from the differential measurement of the direct and reflected code ranges, we investigated the cross-correlated waveforms of the two new BDS-3 civil signals for further exploration. Figures 8 and 9, respectively, show the waveforms of B1C and B2a codes for direct and reflected signals. During the experiment, the sea surface had no appreciable roughness and the reflector heights ranged from three to five meters, so that the path delays can be calculated from the peak positions of the waveforms [6]. From Figures 8 and 9, the direct and reflected B2a waveforms are about half of the B1C ones. This may be caused by its poor signal quality and narrower bandwidth.

**Figure 8.** Cross-correlated waveforms of B1C code for direct (blue) and reflected (red) signals.

**Figure 9.** Cross-correlated waveforms of B2a code for direct (blue) and reflected (red) signals.

Centimeter-level SSH measurements are widely required for many geoscience applications. Obviously, the original solutions derived from B1C and B2a cannot directly satisfy this requirement. However, as BDS-3 has completed its full operations, an adequate number of satellites could be observed for GNSS-R altimetry during our experiment. Their SSH measurements could be obtained continuously and so the change of actual SSH was a steady dynamic process. In this paper, moving averages with windows of one minute and five minutes were applied to smoothing solutions derived from B1C and B2a signals. In Figures 10 and 11, the red points stand for the SSH obtained from radar altimeter; the blue ones stand for those after applying a one-minute moving average; green ones stand for those after applying a five-minute moving average. The results indicated that the precision improved a lot in both cases.

**Figure 10.** SSHs derived from B1C code-level delay measurements with moving average and radar altimeter for more than eight hours.

**Figure 11.** SSHs derived from B2a code-level delay measurements with moving average and radar altimeter for more than eight hours.

In order to evaluate the performance of the filters, we differentiated between the solutions and measurements of the radar altimeter. Figures 12 and 13 show the residuals. The RMSs of B1C-based SSH are 0.090 m and 0.053 m for one-minute and five-minute moving averages while those for B2a case are 0.199 m and 0.111 m. The final results show that centimeter-level SSH can be achieved using the B1C signal, while the precision for the B2a case can only reach the decimeter level.

**Figure 12.** Differences between measured SSHs using monostatic radar and smoothed solutions from B1C signals.

**Figure 13.** Differences between measured SSHs using monostatic radar and smoothed solutions from B2a signals.
