Method and apparatus for determining a channel state of an impaired data channel
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 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 data transmission methods as well.
1. A method of determining a two-dimensional (2D) channel state of an impaired data channel connecting at least one transmitter and at least one receiver, the impaired data channel including at least one reflector having a reflector location, a reflector frequency shift, and at least one coefficient of reflection, the method comprising:
transmitting, by the at least one transmitter, a plurality of Orthogonal Time Frequency Space (OTFS) pilot symbols P pt,pf as OTFS pilot symbol waveform bursts P pt,pf W p (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 selected from a OTFS time-frequency grid, wherein the OTFS pilot symbol waveform bursts P pt,pf W p (pt, pf) are mutually orthogonal waveform bursts derived from cyclically time and frequency shifted versions of a common OTFS pilot basis waveform W p ,
distorting the OTFS pilot symbol waveform bursts into channel-convoluted OTFS pilot bursts based on the impaired data channel, wherein the channel-convoluted OTFS pilot bursts comprise a combination of direct OTFS pilot bursts and replica OTFS pilot bursts, and wherein:
the direct OTFS pilot bursts comprise the plurality of OTFS pilot symbols; and
the replica OTFS pilot bursts comprise direct OTFS pilot bursts reflected off the at least one reflector before reaching the at least one receiver; and
producing direct OTFS waveform bursts based on the reflected direct OTFS pilot bursts, the direct OTFS waveform bursts being further reflector time-delayed and reflector frequency-shifted at the at least one receiver.
2. The method of claim 1 , wherein the channel-convoluted OTFS pilot bursts are received by the at least one receiver using a 2D pilot OTFS time-frequency bin structure with bin sizes and bin coordinate positions proportional to the OTFS time-frequency grid, and wherein the 2D channel state of the impaired data channel is determined based on the channel-convoluted OTFS pilot bursts.
3. The method of claim 2 , wherein the at least one receiver comprises a receiver location and a receiver frequency shift, and wherein the channel-convoluted OTFS pilot bursts further comprises a transmitter frequency shifted direct OTFS pilot burst and a receiver frequency shifted direct OTFS pilot burst.
4. The method of claim 2 , wherein the 2D channel state is at least partially determined based on at least one 2D impulse response indicative of how the impaired data channel causes at least some of the OTFS pilot symbol waveform bursts P t1,f1 W p (t1, f1) transmitted at a first time-frequency coordinate to be projected onto different OTFS pilot symbol waveform bursts P t2,f2 W p (t2, f2) originally transmitted at a different time-frequency coordinate.
5. The method of claim 4 , wherein the at least one 2D impulse response is indicative of the 2D channel state.
6. The method of claim 2 , wherein the 2D channel state comprises a matrix.
7. The method of claim 2 , wherein the plurality of OTFS pilot symbols P pt,pf is known by the at least one receiver, and wherein the plurality of OTFS pilot symbols is further selected to be any of: one-dimensional or two-dimensional m-sequences comprising binary maximal-length shift register sequences, delta values P i,j surrounded by regions of P pt,pf zero values, one-dimensional or two-dimensional Barker codes, Costas arrays, Walsh matrixes, or another plurality of pilot symbols selected for acquiring the 2D channel state.
8. The method of claim 2 , wherein the impaired data channel is an optical fiber data channel.
9. The method of claim 2 , wherein the plurality of OTFS pilot symbols P pt,pf , the OTFS time-frequency grid, and the 2D pilot OTFS time-frequency bin structure are selected so that if the impaired data channel causes at least some of the OTFS pilot symbol waveform bursts P t1,f1 W p (t1, f1) originally transmitted at a first time-frequency coordinate to be projected onto different OTFS pilot symbol waveform bursts P t2,f2 W p (t2, f2) originally transmitted at a different time-frequency coordinate, and bins different from those nominally corresponding to the OTFS pilot symbol waveform bursts P t1,f1 W p (t1, f1), at least some of the projections are detected and quantified by the at least one receiver.
10. The method of claim 9 , wherein the plurality of OTFS pilot symbols P pt,pf transmitted as OTFS pilot symbol waveform bursts P pt,pf W p (pt, pf) comprise at least one non-null OTFS pilot symbol P pt,pf transmitted as an OTFS pilot symbol waveform burst P pt,pf W p (pt, pf) with sufficient power to be detectable by the at least one receiver; and any of:
at least some of the plurality of OTFS pilot symbols are null pilot symbols intended to create empty time pt and frequency pf unique pilot time-frequency coordinates chosen from the OTFS time-frequency grid, where no waveform burst is transmitted; or
at least some of the plurality of OTFS pilot symbols are background pilot symbols that create a uniform background of time pt and frequency pf unique pilot time-frequency coordinates chosen from the OTFS time-frequency grid, such that projections of channel-convoluted non-null OTFS pilot bursts onto the uniform background are detected and quantified by the at least one receiver.
11. An apparatus for determining a two-dimensional (2D) channel state of an impaired data channel connecting at least one transmitter and at least one receiver, the impaired data channel including at least one reflector having a reflector location, a reflector frequency shift, and at least one coefficient of reflection, the apparatus comprising:
a processor in the at least one transmitter; and
a memory storing instructions that, when executed by the processor, causes the apparatus to:
transmit a plurality of Orthogonal Time Frequency Space (OTFS) pilot symbols P pt,pf as OTFS pilot symbol waveform bursts P pt,pf W p (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 selected from a OTFS time-frequency grid, wherein the OTFS pilot symbol waveform bursts P pt,pf W p (pt, pf) are mutually orthogonal waveform bursts derived from cyclically time and frequency shifted versions of a common OTFS pilot basis waveform W p ,
distorting the OTFS pilot symbol waveform bursts into channel-convoluted OTFS pilot bursts based on the impaired data channel, wherein the channel-convoluted OTFS pilot bursts comprise a combination of direct OTFS pilot bursts and replica OTFS pilot bursts, and wherein:
the direct OTFS pilot bursts comprise the plurality of OTFS pilot symbols, and
the replica OTFS pilot bursts comprise direct OTFS pilot bursts reflected off the at least one reflector before reaching the at least one receiver; and
producing direct OTFS waveform bursts based on the reflected direct OTFS pilot bursts, the direct OTFS waveform bursts being further reflector time-delayed and reflector frequency-shifted at the at least one receiver.
12. The apparatus of claim 11 , wherein the channel-convoluted OTFS pilot bursts are received by the at least one receiver using a 2D pilot OTFS time-frequency bin structure with bin sizes and bin coordinate positions proportional to the OTFS time-frequency grid, and wherein the 2D channel state of the impaired data channel is determined based on the channel-convoluted OTFS pilot bursts.
13. The apparatus of claim 12 , wherein the at least one receiver comprises a receiver location and a receiver frequency shift, and wherein the channel-convoluted OTFS pilot bursts further comprises a transmitter frequency shifted direct OTFS pilot burst and a receiver frequency shifted direct OTFS pilot burst.
14. The apparatus of claim 12 , wherein the 2D channel state is at least partially determined based on at least one 2D impulse response indicative of how the impaired data channel causes at least some of the OTFS pilot symbol waveform bursts P t1,f1 W p (t1, f1) transmitted at a first time-frequency coordinate to be projected onto different OTFS pilot symbol waveform bursts P t2,f2 W p (t2, f2) originally transmitted at a different time-frequency coordinate.
15. The apparatus of claim 14 , wherein the at least one 2D impulse response is indicative of the 2D channel state.
16. The apparatus of claim 12 , wherein the 2D channel state comprises a matrix.
17. The apparatus of claim 12 , wherein the plurality of OTFS pilot symbols P pt,pf is known by the at least one receiver, and wherein the plurality of OTFS pilot symbols is further selected to be any of: one-dimensional or two-dimensional m-sequences comprising binary maximal-length shift register sequences, delta values P i,j surrounded by regions of P pt,pf zero values, one-dimensional or two-dimensional Barker codes, Costas arrays, Walsh matrixes, or another plurality of pilot symbols selected for acquiring the 2D channel state.
18. The apparatus of claim 12 , wherein the impaired data channel is an optical fiber data channel.
19. The apparatus of claim 12 , wherein the plurality of OTFS pilot symbols P pt,pf , the OTFS time-frequency grid and the 2D pilot OTFS time-frequency bin structure are selected so that if the impaired data channel causes at least some of the OTFS pilot symbol waveform bursts P t1,f1 W p (t1, f1) originally transmitted at a first time-frequency coordinate to be projected onto different OTFS pilot symbol waveform bursts P t2,f2 W p (t2, f2) originally transmitted at a different time-frequency coordinate, and bins different from those nominally corresponding to the OTFS pilot symbol waveform bursts P t1,f1 W p (t1, f1), at least some of the projections are detected and quantified by the at least one receiver.
20. The apparatus of claim 19 , wherein the plurality of OTFS pilot symbols P pt,pf transmitted as OTFS pilot symbol waveform bursts P pt,pf W p (pt, pf) comprise at least one non-null OTFS pilot symbol P pt,pf transmitted as an OTFS pilot symbol waveform burst P pt,pf W p (pt, pf) with sufficient power to be detectable by the at least one receiver; and any of:
at least some of the plurality of OTFS pilot symbols are null pilot symbols intended to create empty time pt and frequency pf unique pilot time-frequency coordinates chosen from the OTFS time-frequency grid, where no waveform burst is transmitted; or
at least some of the plurality of OTFS pilot symbols are background pilot symbols that create a uniform background of time pt and frequency pf unique pilot time-frequency coordinates chosen from the OTFS time-frequency grid, such that projections of channel-convoluted non-null OTFS pilot bursts onto the uniform background are detected and quantified by the at least one receiver.