Based on the carrier’s attitude information (obtained from the onboard inertial navigation system), the satellite’s position (calculated from orbital ephemeris), and the carrier’s position (determined via GPS), the antenna controller can compute the antenna beam pointing angles (azimuth and elevation). The antenna servo mechanism drives the antenna motors to rotate accordingly, ensuring that the antenna beam center is geometrically aligned with the satellite.
However, even when the antenna beam center is aligned with the satellite, proper reception of the satellite signal is not guaranteed, as polarization angle matching is also required.
What is the Antenna Polarization Angle?
Polarization Angle: Refers to the angle between the electric field vector of the satellite downlink signal and the local horizontal plane of the ground antenna.
Why does the antenna polarization angle exist? The antenna polarization angle arises from the geometric relationship between the satellite and the ground antenna itself.
- Geostationary satellites are typically positioned above the equator. The signals transmitted by the satellite can have horizontal polarization as well as vertical polarization.The polarization of the signal emitted by the satellite antenna (e.g., “vertical polarization”) is defined relative to the Earth’s equatorial plane. Below are common frequencies and polarizations of beacon signals transmitted by satellites, where V represents vertical polarization and H represents horizontal polarization.
Satellite Beacon Signal
- Because the Earth is a sphere, every ground antenna at any location on the Earth’s surface has its own local horizontal plane.
- When the “vertical polarization” direction of a satellite signal is projected onto the local horizontal reference frame of the ground antenna, it is not perfectly vertical, resulting in a tilt angle—this is the origin of the polarization angle.Therefore, except for regions located exactly on the meridian directly beneath the satellite (the sub-satellite point), almost all ground antennas experience some polarization angle when receiving satellite signals.
- Polarization angle is defined as the rotation angle required for the ground antenna to align with the polarization direction of the satellite signal. Without this adjustment, polarization mismatch occurs, significantly reducing signal reception efficiency.
We can use an illustrative example to explain the relationship between antenna elevation angle, azimuth angle, and polarization angle:
Consider the satellite downlink signal as a lock’s keyhole, and the antenna feed as a key.
- Azimuth and elevation anglesalign the antenna with the satellite, which is equivalent to precisely pointing the key toward the keyhole. However, simply inserting the key into the keyhole does not open the lock.
- Rotating the polarization angleis like turning the key after it is inserted. When the key’s teeth align perfectly with the lock mechanism, the lock opens. Conversely, if the teeth do not match, the lock cannot be opened.
Similarly, if the antenna’s polarization angle does not match the direction of the satellite signal’s electric field vector, polarization mismatch occurs, and the antenna cannot receive the signal with maximum efficiency. If the polarization deviation reaches 90°, the antenna barely receives any signal, potentially causing communication interruption.
Example Illustration:
Assume a ground antenna is located in Beijing and needs to point to a geostationary satellite above the equator, with a longitude west of Beijing. The satellite transmits a signal with vertical polarization, which is defined as vertical relative to the equatorial plane.
- To align the antenna with the satellite, the azimuth anglemust point toward the southwest, and the elevation angle must be raised to a certain value, completing the geometric alignment with the satellite.
- When the satellite signal reaches the ground antenna, it is tilted 20° downward to the rightrelative to the antenna’s local horizontal plane. Therefore, the antenna feed (LNB) must be rotated 20° in the opposite direction (counterclockwise) to compensate.
How is the Polarization Angle Calculated?
Discussion:
Consider a scenario where an antenna is mounted on a vehicle tracking a geostationary satellite. Initially, the vehicle is stationary, and the antenna servo system has adjusted the azimuth, elevation, and polarization angles to align with the satellite. Then, the vehicle starts moving at 100 km/h. During motion, the antenna continues to adjust azimuth and elevation angles to maintain alignment with the satellite. However, if the polarization angle is not adjusted, how much does it change as the vehicle moves?
A qualitative calculation can be performed as follows:
Construct a triangle with the satellite, the vehicle’s starting point, and the vehicle’s position after 1 hour:
- Vertex A:The geostationary satellite.
- Vertex B:The vehicle’s starting point.
- Vertex C:The vehicle’s position after 1 hour.
In this triangle, the sides AB and AC are both approximately 36,000 km, while the side BC is only 100 km. From the perspective of vertex A (the satellite), the angle between points B and C (the angular displacement) is extremely small.
Since the polarization angle is determined by the relative geometry between the antenna and the satellite, a 100 km movement of the vehicle causes only a negligible change in the antenna–satellite geometry, and therefore the change in polarization angle is also very small.
Quantitative Calculation:
Polarization Angle Calculation Formula
According to Satellite Communications by Timothy Pratt, Charles W. Bostian, and Jeremy E. Allnutt, the polarization angle of a ground antenna can be calculated as follows:
Where:
ϕ is the latitude of the ground antenna (positive for north, negative for south), Δλ is the difference in longitude between the satellite’s sub-satellite point and the ground antenna location.
When the satellite longitude and the ground antenna longitude are the same, Δλ = 0, ψ = arctan [ sin(0) / tan(φ) ] = arctan(0) = 0°. At this moment, the ground antenna’s polarization angle is 0°.
Case Illustration: How Much Does the Polarization Angle Change When the Antenna Moves 100 km?
Scenario Setup:
- Satellite position:Geostationary satellite at longitude 101°E.
- Vehicle initial position (Point A):Latitude 40°N, Longitude 85°E.
- Vehicle movement:Along longitude 85°E, heading due north for 100 km.
Calculation Process:
- Compute longitude difference (Δλ):
The longitude difference is defined as the difference between the ground antenna’s longitude and the satellite’s longitude. In this scenario, the vehicle’s longitude does not change during the journey, so Δλ remains constant: Δλ=λ_ant−λ_sat = 85°−101°=−16°
- Compute latitude change
The distance corresponding to one degree of latitude on Earth is approximately 111.32 km. The change in latitude can be calculated as Δφ ≈ 100 km / 111.32 km/° ≈ 0.898°. For simplicity, we can approximate this as 0.9°. Therefore, the latitude of the car’s destination (point B) is φ_B = φ_A + Δφ = 40° + 0.9° = 40.9°.
- Calculate the polarization angle at point A
- Calculate the polarization angle at point B
- Change in polarization angle
Δψ = ψ_B – ψ_A = -17.66° – ( -18.18° ) = 0.52°. When the carrier moves 100 km, the polarization angle changes by 0.52°. Similarly, we can calculate that when the carrier moves 1000 km, the polarization angle changes by 4.8°. Calculation flowchart:
The polarization angle is also related to the carrier’s attitude.
Let’s discuss this issue: When the carrier’s attitude changes, the antenna servo system first adjusts the antenna pointing according to the carrier’s attitude changes to ensure that the antenna beam center always points to the satellite. In this case, how many degrees does the polarization angle change due to the attitude?
While the antenna azimuth/elevation servo system compensates for attitude changes to maintain the antenna pointing toward the satellite, it cannot automatically correct the polarization angle error caused by the attitude change. Therefore, the polarization angle deviation is not eliminated.
Assume the carrier attitude changes are:
• Δr: roll angle change
• Δp: pitch angle change
• Δy: yaw angle change
The antenna pointing angles calculated based on the carrier attitude, satellite position, and antenna location are:
• Az: azimuth
• El: elevation
The effect of attitude changes on the polarization angle (ΔPol) can be calculated using the following classical kinematic approximation formula.
To simplify and focus on the main effects, in many dynamic antenna control applications, when the azimuth angle Az is not near 0° or 180°, we have sin(Az) ≈ 1 and cos(Az) ≈ 0. Under this assumption, the above formula can be further simplified as:
From the above formula, we can see:
- Roll angle changesof the carrier are the most direct and significant component affecting the polarization angle. Changes in the carrier’s roll angle almost translate one-to-one into polarization angle changes.
- Yaw angle effectsare related to the antenna’s elevation angle:
When El = 0° (antenna pointing horizontally toward the horizon): sin(El) = 0, so yaw has no effect on the polarization angle.
• When El = 90° (antenna pointing vertically toward the zenith): sin(El) = 1, so ΔPol ≈ Δr + Δy. - Pitch angle changesof the carrier have relatively minor effects on the polarization angle.
Below are several typical scenarios showing how carrier attitude changes affect the polarization angle.
|
Scenario |
Carrier Attitude Change |
Antenna Elevation (El) |
Main Influencing Component |
Required Polarization Correction ΔPol (approx.) |
|
Scenario 1: Ship in wind |
Roll Δr = +10° (Pitch Δy ≈ 0) |
30° |
Roll-dominated |
10° + 0 * sin(30°) = 10° |
|
Scenario 2: Aircraft entering a turn |
Yaw Δy = +20° (Roll already compensated by antenna) |
45° |
Yaw-dominated |
0 + 20° * sin(45°) = 14.1° |
|
Scenario 3: Car rotating on overpass |
Yaw Δy = +90° (90° turn) |
60° (satellite position relatively high) |
Yaw effect significant |
0 + 90° * sin(60°) = 77.9° |
! If these changes are not compensated in real time, they can cause severe polarization mismatch, and may even lead to communication interruption!
Conclusion
|
Key Point |
Content |
|
✔ Polarization angle is one of the essential matching conditions for signal reception |
Relying on azimuth + elevation angle to point to the satellite alone is not sufficient |
|
✔ Polarization changes with ground position |
Latitude difference of 16°, polarization angle can vary by several degrees |
|
✔ Polarization is also affected by carrier attitude |
Especially roll and yaw angles |
|
✔ Polarization deviation caused by attitude changes cannot be automatically compensated by the servo system |
Must be corrected by the control algorithm |
