# Increasing the Number of Sea Surface Reflected Signals Received by GNSS-Reflectometry Altimetry Satellite Using the Nadir Antenna Observation Capability Optimization Method

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## Abstract

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## 1. Introduction

## 2. Data Sets

#### 2.1. TDS-1 Space GPS Receiver Remote Sensing Instrument Data Collections

- The SNR of the peak DDM. This data is recorded in the metadata.nc file of the L1 products and is used to verify the accuracy of NASNRM.
- The nadir antenna gain map. The gain of the antenna in different directions is not the same. For better simulation calculation in Section 4.1, the TDS-1 nadir antenna gain map file is used to calculate the SNR.
- TDS-1 satellite ephemeris. Since TDS-1 products have been a threshold in terms of signal channel number, it is not possible to obtain all available SPs information within a period of time through this product. Based on this restriction, the SPs information is recalculated. In order to avoid errors introduced by the orbital simulation, the coordinates of the TDS-1 in the L1 product are used.
- Wind speed. In order to calculate the weight of different wind speeds in a period of time, this paper gets the wind speed information from the TDS-1 observation based on the ‘L2_FDI.nc’ in the L2 product.

#### 2.2. Global Navigation Satellite System Precision Ephemeris

## 3. Methodology

#### 3.1. The Nadir Antenna Signal-to-Noise Ratio Model (NASNRM)

#### 3.2. The Specular Point Filtering Algorithm (SPFA)

- When $\theta ={0}^{\xb0}$, ${\alpha}_{\mathrm{min}}={90}^{\xb0}-\gamma /2$, ${\alpha}_{\mathrm{max}}={90}^{\xb0}$;
- When $\theta <\gamma /2$, ${\alpha}_{\mathrm{min}}={90}^{\xb0}-\left(\theta +\gamma /2\right)$, ${\alpha}_{\mathrm{max}}={90}^{\xb0}$;
- When $\theta >\gamma /2$, ${\alpha}_{\mathrm{min}}={90}^{\xb0}-\left(\theta +\gamma /2\right)$, ${\alpha}_{\mathrm{max}}={90}^{\xb0}-\left(\theta -\gamma /2\right)$.

## 4. Results and Discussions

#### 4.1. The Signal-to-Noise Ratio of Received Reflected Signals

- As the elevation angle increases, the SNR increases. This is because as the elevation angle increases, the length of the GNSS signal propagation path is reduced, which in turn reduces the power loss due to signal propagation. At the same time, the higher the elevation angle, the stronger the scattering ability of the signal on the sea surface. When the elevation angle at the range of 0 to 10 degrees, the SNR increases obviously. As the elevation angle increases gradually, the change gradually becomes gentle. This indicates that SNR is sensitive to the change of the elevation angle in a low angle range, while SNR is less affected by the change of the elevation angle in a medium and high angle range. This can provide a reference for the parameter setting of future GNSS-R spaceborne multi-channel antenna.
- In order to ensure the quality of the observation, the TDS-1 has threshold settings at both the elevation angle (~45°) and the SNR (~−10 dB). The SNR obtained from NASNRM is consistent with the trend of TDS-1 observations, and the values are also in the same order of magnitude.

- The calculated SNR is based on the wave spectrum. However, there is still a difference between the real sea conditions and the sea surface simulated according to the wave spectrum.
- The measured antenna temperature mainly ranges from 300 to 800 K. In this paper, the antenna temperature is set to 550 K when calculating SNR. This may cause the results to deviate from the actual measurement.
- The effect of the TDS-1 attitude is not taken into account when calculating the SNR, which may be biased when using the gain of nadir antenna.
- The transmission power of different GPS satellites is different, and there is also a problem that the transmission power changes with time with the GPS IIF satellite. This factor is not considered in the calculation.

#### 4.2. Minimum Elevation Angle That Meets SNR Requirements

#### 4.3. The Number of Received Reflected Signals

- Under different wind speeds, as the antenna gain and the pointing angle increase, the number of SPs can be peaked. This shows that the reasonable design of antenna gain and pointing angle can optimize the number of received GNSS-R altimetry reflected signals.
- When the pointing angle is constant, the number of SPs can be increased first as the antenna gain increases, and then gradually decreases after reaching the peak. This is because the initial increase in antenna gain will increase the weak signal power, so that more reflected signals are captured by the antenna. The number of signals increased is more than the number of signals decreased by the decrease in the antenna operating range (HPBW reduction) due to the increase of antenna gain. When the two parts are equal, the number of available SPs can reach the peak value. As the antenna gain continues to increase, the number of signals increased due to the increase in power is gradually less than the number of signals reduced due to the diminish in the antenna view field, and the number of available SPs gradually decreased.
- When the antenna gain is low, the number of available SPs gradually decreases as the pointing angle increases. This is because the increase of the pointing angle causes the signal propagation path to become longer and causes more power loss, so that some signals cannot be captured by the low-gain antenna. When the antenna gain is high, the number of available SPs will reach the peak and then gradually decrease with the increase of the pointing angle. This is because the increase of the pointing angle will increase the coverage area of the antenna. Although the increase of the angle will lengthen the signal propagation path and cause more power loss, which will make some signals unable to be captured, the increase of the angle will also make more reflection signals received by the high-gain antenna, thus increasing the number of available SPs. When the number of available SPs reaches its peak, compared to the number of reflected signals that are increased due to the increase in angle, the number of signals that cannot meet the SNR requirement due to the longer signal propagation path is larger, which ultimately leads to the decrease of the number of available SPs.

#### 4.4. The Nadir Antenna Parameters Combination Optimization

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The GNSS-R specular point positioning geometry, where $O$ is the geo-center, $P$ is the position of the specular point, $\alpha $ is elevation angle, ${R}_{E}$ is Earth radius, ${H}_{T}$ and ${H}_{R}$ are the satellite orbital altitude of GNSS and GNSS-R, respectively. ${R}_{TP}$ is the signal transmission distance from GNSS satellite to the specular point, ${R}_{PR}$ is the signal reception distance from GNSS-R satellite to the specular point.

**Figure 2.**Relationship between elevation angle and Fresnel reflection coefficient (right hand circularly polarized (RHCP) turns to left hand circularly polarized (LHCP)).

**Figure 3.**The Geometric relationship between half-power beam width (HPBW) and pointing angle: (

**a**) $\theta ={0}^{\xb0}$, (

**b**) $\theta <\gamma /2$, (

**c**) $\theta >\gamma /2$. Where $R$ is the GNSS-R satellite, $O$ is the geo-center, $\theta $ is the pointing angle, $\gamma $ and $\phi $ are horizontal and vertical HPBW, respectively, ${\alpha}_{\mathrm{min}}$ and ${\alpha}_{\mathrm{max}}$ are represent the maximum and minimum elevation angle. To simplify the analysis, $\gamma =\phi $.

**Figure 4.**The SNR obtained according to nadir antenna signal-to-noise ratio model (NASNRM) as a function of the elevation angle. The $U10$ is the wind speed at 10 m height above the sea surface. The inset is the SNR when the elevation angle at the range of 45 to 90 degrees.

**Figure 5.**The relationship between the minimum elevation angle and the gain. The $U10$ is the wind speed at 10 m height above the sea surface.

**Figure 6.**The relationship between the number of received reflection signals and antenna gain and pointing angle with respect to different wind speeds. The $U10$ is the wind speed at 10 m height above the sea surface.

**Table 1.**Related parameter settings when calculating signal-to-noise ratio (SNR) through Equation (6).

Parameter | Value |
---|---|

Orbital altitude of GPS satellite | 20200 |

Orbital altitude of GNSS-R satellite (km) | 635 |

Pointing angle (°) | 0 |

Antenna peak gain (dBi) | 13.3 |

Antenna gain pattern | TDS-1 nadir antenna gain map |

Signal frequency (MHz) | 1575.42 |

Signal wavelength (m) | 0.19 |

Coherent integration time (ms) | 1 |

Antenna temperature (K) | 550 |

Noise bandwidth (Hz) | 1000 |

Integration area (km × km) | 100 × 100 |

Sampling size (m × m) | 100 × 100 |

Integration approach | Numerical integration |

U10 (m/s) | 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Standard deviation (dB) | 0.70 | 0.71 | 0.69 | 0.62 | 0.73 | 0.85 | 1.12 | 0.92 | 1.22 | 1.32 | 1.54 | 1.59 |

**Table 3.**Optimal parameters combination for nadir antenna observation capability with different sea surface wind speeds.

Wind Speed U10 (m/s) | Antenna Gain (dBi) | Pointing Angle $\mathit{\theta}$ | Received Signal Quantity (Count) | Reflected Signal Utilization (%) |
---|---|---|---|---|

1 | 16.80 | 30.02 | 21068 | 19.85 |

3 | 18.18 | 31.02 | 20670 | 19.47 |

5 | 19.02 | 31.54 | 20055 | 18.89 |

7 | 20.00 | 31.96 | 19925 | 18.77 |

9 | 20.33 | 32.01 | 19507 | 18.38 |

11 | 20.97 | 32.58 | 19473 | 18.34 |

13 | 21.35 | 32.99 | 19004 | 17.90 |

15 | 21.77 | 32.78 | 18756 | 17.67 |

17 | 21.98 | 32.78 | 18597 | 17.52 |

19 | 22.60 | 33.83 | 18488 | 17.42 |

21 | 22.87 | 33.46 | 18399 | 17.33 |

23 | 23.19. | 33.46 | 18299 | 17.24 |

Parameter Combination | Antenna Gain (dBi) | Pointing Angle $\mathit{\theta}$ | Received Signal Quantity (Count) | Reflected Signal Utilization (%) |
---|---|---|---|---|

Optimization parameters | 20.94 | 32.82 | 19104 | 18.00% |

TDS-1 satellite nadir antenna parameters | 13.30 | 0 | 2994 | 2.82% |

Optimized parameters using TDS-1 nadir antenna gain | 13.30 | 20.23 | 4390 | 4.14% |

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## Share and Cite

**MDPI and ACS Style**

Liu, Z.; Zheng, W.; Wu, F.; Kang, G.; Li, Z.; Wang, Q.; Cui, Z.
Increasing the Number of Sea Surface Reflected Signals Received by GNSS-Reflectometry Altimetry Satellite Using the Nadir Antenna Observation Capability Optimization Method. *Remote Sens.* **2019**, *11*, 2473.
https://doi.org/10.3390/rs11212473

**AMA Style**

Liu Z, Zheng W, Wu F, Kang G, Li Z, Wang Q, Cui Z.
Increasing the Number of Sea Surface Reflected Signals Received by GNSS-Reflectometry Altimetry Satellite Using the Nadir Antenna Observation Capability Optimization Method. *Remote Sensing*. 2019; 11(21):2473.
https://doi.org/10.3390/rs11212473

**Chicago/Turabian Style**

Liu, Zongqiang, Wei Zheng, Fan Wu, Guohua Kang, Zhaowei Li, Qingqing Wang, and Zhen Cui.
2019. "Increasing the Number of Sea Surface Reflected Signals Received by GNSS-Reflectometry Altimetry Satellite Using the Nadir Antenna Observation Capability Optimization Method" *Remote Sensing* 11, no. 21: 2473.
https://doi.org/10.3390/rs11212473