System and method for doppler compensation using a second derivative
An illustrated embodiment disclosed herein is a method including determining, by an endpoint, a Doppler frequency offset and a first derivative of the Doppler frequency offset, calculating, by the endpoint, a second derivative of the Doppler frequency offset based on an orbital model, and calculating, by the endpoint, a first delta to the Doppler frequency offset and a second delta to the first derivative of the Doppler frequency offset.
1. A method comprising:
determining, by an endpoint, a Doppler frequency offset and a first derivative of the Doppler frequency offset;
calculating, by the endpoint, a second derivative of the Doppler frequency offset based on an orbital model;
calculating, by the endpoint, a first delta to the Doppler frequency offset and a second delta to the first derivative of the Doppler frequency offset based on the second derivative;
updating the Doppler frequency offset and the first derivative of the Doppler frequency offset based on the first delta and the second delta; and
transmitting, to a satellite, a physical data unit (PDU) using the updated Doppler frequency offset and the updated first derivative of the Doppler frequency offset.
2. The method of claim 1 , wherein the orbital model is a function of the Doppler frequency offset, a first derivative of the Doppler frequency offset, and an altitude of a satellite in communication with the endpoint.
3. The method of claim 1 , further comprising receiving one or more swept syncs from a satellite in communication with the endpoint, wherein the Doppler frequency offset and a first derivative of the Doppler frequency offset are determined based on receiving the one or more swept syncs.
4. The method of claim 3 , wherein the Doppler frequency offset is determined based on extrapolating a frequency from one or more times of the one or more swept syncs to a different time.
5. The method of claim 3 , wherein the second first delta and the second delta are calculated based on a frame duration between a first of the one or more swept syncs and a second of the one or more swept syncs.
6. The method of claim 3 , wherein the second first delta and the second delta are calculated based on a delta between a time at which the endpoint receives one of the one or more swept syncs and a second time at which the endpoint sends a second PDU to the satellite.
7. The method of claim 6 , wherein the delta depends on which slot of an uplink (UL) frame the PDU is in.
8. The method of claim 1 , further comprising calculating a first sum of the first delta to the Doppler frequency offset and calculating a second sum of the second delta to the first derivative of the Doppler frequency offset.
9. The method of claim 8 , wherein the first sum and the second sum are determined for a time when the endpoint sends the PDU to a satellite.
10. An endpoint comprising a processor having programmed instructions that when executed cause the processor to:
determine a Doppler frequency offset and a first derivative of the Doppler frequency offset;
calculate a second derivative of the Doppler frequency offset based on an orbital model;
calculate a first delta to the Doppler frequency offset and a second delta to the first derivative of the Doppler frequency offset based on the second derivative;
update the Doppler frequency offset and the first derivative of the Doppler frequency offset based on the first delta and the second delta; and
transmit, to a satellite, a physical data unit (PDU) using the updated Doppler frequency offset and the updated first derivative of the Doppler frequency offset.
11. The endpoint of claim 10 , wherein the orbital model is a function of the Doppler frequency offset, a first derivative of the Doppler frequency offset, and an altitude of a satellite in communication with the endpoint.
12. The endpoint of claim 10 , the processor having further programmed instructions to receive one or more swept syncs from a satellite in communication with the endpoint, wherein the Doppler frequency offset and a first derivative of the Doppler frequency offset are determined based on receiving the one or more swept syncs.
13. The endpoint of claim 12 , wherein the Doppler frequency offset is determined based on extrapolating a frequency from one or more times of the one or more swept syncs to a different time.
14. The endpoint of claim 12 , wherein the second first delta and the second delta are calculated based on a frame duration between a first of the one or more swept syncs and a second of the one or more swept syncs.
15. The endpoint of claim 12 , wherein the second first delta and the second delta are calculated based on a delta between a time at which the endpoint receives one of the one or more swept syncs and a second time at which the endpoint sends a second PDU to the satellite.
16. The endpoint of claim 15 , wherein the delta depends on which slot of an uplink (UL) frame the PDU is in.
17. The endpoint of claim 10 , the processor having further programmed instructions to:
calculate a first sum of the first delta to the Doppler frequency offset; and
calculate a second sum of the second delta to the first derivative of the Doppler frequency offset.
18. The endpoint of claim 17 , wherein the first sum and the second sum are determined for a time when the endpoint sends the PDU to a satellite.
19. The endpoint of claim 10 , the processor having further programmed instructions to determine the Doppler frequency offset and the first derivative of the Doppler frequency offset by:
receiving a signal;
derotating the signal; and
detecting energy in the signal.
20. The endpoint of claim 10 , wherein the satellite reduces a search space for the PDU.