OTFS methods of data channel characterization and uses thereof
Fiber, cable, and wireless data channels are typically impaired by reflectors and other imperfections, producing a channel state with echoes and frequency shifts in data waveforms. Here, methods of using OTFS pilot symbol waveform bursts to automatically produce a detailed 2D model of the channel state are presented. This 2D channel state can then be used to, optimize data transmission. For wireless data channels, an even more detailed 2D model of channel state can be produced by using polarization and multiple antennas in the process. Once 2D channel states are known, the system turns imperfect data channels from a liability to an advantage by using channel imperfections to boost data transmission rates. The methods can be used to improve legacy data transmission modes in multiple types of media, and are particularly useful for producing new types of robust and high capacity wireless communications using non-legacy OTFS data transmission methods.
1. A method for determining at least one two-dimensional (2D) channel state of an impaired data channel connecting at least one transmitter and at least one receiver, the at least one transmitter comprising T transmitting antennas and the at least one receiver comprising R receiving antennas, the impaired data channel comprising at least one reflector, the at least one reflector comprising a reflector location, a reflector frequency shift and at least one coefficient of reflection, the method comprising:
receiving, using the R receiving antennas, channel-convoluted orthonormal time-frequency shifting (OTFS) pilot bursts using a 2D pilot OTFS time-frequency bin structure with bin sizes and bin-coordinate positions proportional to an OTFS time-frequency grid; and
determining the at least one 2D channel state of the impaired data channel based on the channel-convoluted OTFS pilot bursts,
wherein the channel-convoluted OTFS pilot bursts comprise a combination of direct OTFS pilot bursts and replica OTFS pilot bursts,
wherein the direct OTFS pilot bursts comprise a plurality of OTFS pilot symbols P sn,pt,pf in a stream sn transmitted from one of the T transmitting antennas to one of the R receiving antennas,
wherein the plurality of OTFS pilot symbols are transmitted as OTFS pilot symbol waveform bursts P sn,pt,pf ·Wp(pt, pf) over a plurality of combinations of times pt and frequencies pf, where each of the times pt and the frequencies pf are unique pilot time-frequency coordinates chosen from the OTFS time-frequency grid,
wherein the OTFS pilot symbol waveform bursts P sn,pt,pf ·Wp(pt, pf) are mutually orthogonal waveform bursts derived from cyclically time and frequency shifted versions of a common OTFS pilot basis waveform Wp,
wherein the direct OTFS pilot bursts travel directly from the at least one transmitter to the at least one receiver,
wherein the replica OTFS pilot bursts comprise direct OTFS pilot bursts that have reflected off the at least one reflector before reaching the at least one receiver, thereby producing direct OTFS waveform bursts that are further reflector time-delayed and reflector frequency-shifted at the at least one receiver, and
wherein the at least one transmitter is configured to transmit the OTFS pilot symbol waveform bursts using the T transmitting antennas.
2. The method of claim 1 , wherein the at least one 2D channel state comprises up to R different 2D channel states.
3. The method of claim 2 , wherein the R receiving antennas are spatially separated.
4. The method of claim 1 , wherein each of the at least one 2D channel state comprises a matrix or other mathematical transform describing how signals transmitted by one of the T transmitting antennas are coupled with signals from the at least one transmitter that are received by one of the R receiving antennas.
5. The method of claim 1 , wherein T>1 and R>1, and wherein R≥T.
6. The method of claim 1 , wherein the T transmitting antennas and the R receiving antennas are directional antennas, and wherein the directional antennas are configured to minimize cross-talk between different sets of the T transmitting antennas and the R receiving antennas.
7. The method of claim 1 , wherein the OTFS pilot symbol waveform bursts are transmitted using the T transmitting antennas over a same frequency range.
8. The method of claim 1 , wherein the impaired data channel is an optical fiber data channel comprising at least one optical fiber, an electrically conducting wire data channel comprising at least one metallic electrical conductor, or a data channel comprising a fluid.
9. The method of claim 1 , wherein the plurality of channel-convoluted data bursts corresponds to a plurality of data symbols transmitted by the at least one transmitter, and wherein the method further comprises:
deconvoluting, for each of the R receiving antennas, at least some of the plurality of channel-convoluted data bursts to derive an approximation of the plurality of data symbols.
10. An apparatus for determining at least one two-dimensional (2D) channel state of an impaired data channel connecting at least one transmitter and at least one receiver, the at least one transmitter comprising T transmitting antennas and the at least one receiver comprising R receiving antennas, the impaired data channel comprising at least one reflector, the at least one reflector comprising a reflector location, a reflector frequency shift and at least one coefficient of reflection, the apparatus comprising:
a processor; and
a memory comprising processor executable code, the processor executable code when executed by the processor causes the processor to:
receive, using the R receiving antennas, channel-convoluted orthonormal time-frequency shifting (OTFS) pilot bursts using a 2D pilot OTFS time-frequency bin structure with bin sizes and bin-coordinate positions proportional to an OTFS time-frequency grid; and
determine the at least one 2D channel state of the impaired data channel based on the channel-convoluted OTFS pilot bursts,
wherein the channel-convoluted OTFS pilot bursts comprise a combination of direct OTFS pilot bursts and replica OTFS pilot bursts,
wherein the direct OTFS pilot bursts comprise a plurality of OTFS pilot symbols P sn,pt,pf in a stream sn transmitted from one of the T transmitting antennas to one of the R receiving antennas,
wherein the plurality of OTFS pilot symbols are transmitted as OTFS pilot symbol waveform bursts P sn,pt,pf ·Wp(pt, pf) over a plurality of combinations of times pt and frequencies pf, where each of the times pt and the frequencies pf are unique pilot time-frequency coordinates chosen from the OTFS time-frequency grid,
wherein the OTFS pilot symbol waveform bursts P sn,pt,pf ·Wp(pt, pf) are mutually orthogonal waveform bursts derived from cyclically time and frequency shifted versions of a common OTFS pilot basis waveform Wp,
wherein the direct OTFS pilot bursts travel directly from the at least one transmitter to the at least one receiver,
wherein the replica OTFS pilot bursts comprise direct OTFS pilot bursts that have reflected off the at least one reflector before reaching the at least one receiver, thereby producing direct OTFS waveform bursts that are further reflector time-delayed and reflector frequency-shifted at the at least one receiver, and
wherein the at least one transmitter is configured to transmit the OTFS pilot symbol waveform bursts using the T transmitting antennas.
11. The apparatus of claim 10 , wherein the at least one 2D channel state comprises up to R different 2D channel states.
12. The apparatus of claim 11 , wherein the R receiving antennas are spatially separated.
13. The apparatus of claim 10 , wherein each of the at least one 2D channel state comprises a matrix or other mathematical transform describing how signals transmitted by one of the T transmitting antennas are coupled with signals from the at least one transmitter that are received by one of the R receiving antennas.
14. The apparatus of claim 10 , wherein T>1 and R>1, and wherein R≥T.
15. The apparatus of claim 10 , wherein the T transmitting antennas and the R receiving antennas are directional antennas, and wherein the directional antennas are configured to minimize cross-talk between different sets of the T transmitting antennas and the R receiving antennas.
16. The apparatus of claim 10 , wherein the OTFS pilot symbol waveform bursts are transmitted using the T transmitting antennas over a same frequency range.
17. The apparatus of claim 10 , wherein the impaired data channel is an optical fiber data channel comprising at least one optical fiber, an electrically conducting wire data channel comprising at least one metallic electrical conductor, or a data channel comprising a fluid.
18. The apparatus of claim 10 , wherein the plurality of channel-convoluted data bursts corresponds to a plurality of data symbols transmitted by the at least one transmitter, and wherein the processor is further configured to:
deconvolute, for each of the R receiving antennas, at least some of the plurality of channel-convoluted data bursts to derive an approximation of the plurality of data symbols.
19. The apparatus of claim 18 , wherein the plurality of data symbols is transmitted by any of Time Division Multiple Access (TDMA), Global System for Mobile Communications (GSM), Frequency Division Multiple Access (FDMA), Orthogonal Frequency Division Multiplexing (OFDM), Code Division Multiple Access (CDMA), OTFS wireless waveform bursts, or other types of wireless waveform bursts.