ORTHOGONAL TIME FREQUENCY SPACE MODULATION OVER A PLURALITY OF NARROW BAND SUBCARRIERS

• US 20180205481A1
• Filed: 07/12/2016
• Published: 07/19/2018
• Est. Priority Date: 07/12/2015
• Status: Active Grant

• Current Assignee: Cohere Technologies Inc
• Original Assignee: Cohere Technologies Inc
• Inventors: Shlomo, Selim Rakib, Hadani, Ronny
• Granted Patent: US 10,693,581 B2
• Time in Patent Office: Days
• CPC Class Codes: H04J 11/00 Orthogonal multiplex systems, e.g. using WALSH codesH04J13/00 takes precedence
• CPC Class Codes: H04J 11/0026 of multi-user interference
• CPC Class Codes: H04J 2011/0003 Combination with other multiplexing techniques
• CPC Class Codes: H04L 23/02 adapted for orthogonal signalling
• CPC Class Codes: H04L 27/2639 Modulators using other transforms, e.g. discrete cosine transforms, Orthogonal Time Frequency and Space [OTFS] or hermetic transforms
• CPC Class Codes: H04L 27/2697 in combination with other modulation techniques
• CPC Class Codes: H04L 5/0016 Time-frequency-code

Abstract

An Orthogonal Time Frequency Space Modulation (OTFS) modulation scheme that maps data symbols, along with optional pilot symbols, using a symplectic-like transformation such as a 2D Fourier transform and optional scrambling operation, into a complex wave aggregate and be backward compatible with legacy OFDM systems, is described. This wave aggregate may be processed for transmission by selecting portions of the aggregate according to various time and frequency intervals. The output from this process can be used to modulate transmitted waveforms according to various time intervals over a plurality of narrow-band subcarriers, often by using mutually orthogonal subcarrier “tones” or carrier frequencies. The entire wave aggregate may be transmitted over various time intervals. At the receiver, an inverse of this process can be used to both characterize the data channel and to correct the received signals for channel distortions, thus receiving a clear form of the original data symbols.

Claims

1. A method of transmitting and receiving, on a per-frame basis, a plurality of data symbols over an impaired wireless channel comprising a plurality of narrow-band subcarriers, the method comprising:

for each frame, using at least one processor to distribute the plurality of data symbols over a 2D OTFS delay-Doppler frame by assigning each data symbol to its own unique 2D OTFS delay-Doppler frame location;

OTFS transforming the data symbols on the 2D OTFS delay-Doppler frame by using each data symbol and frame location to modulate a unique, location specific, 2D basis wave function selected from a set of mutually orthogonal 2D basis wave functions operating over a 2D OTFS time-frequency frame, the transformation also spreading each data symbol, in a lossless and invertible manner, throughout substantially all of the 2D OTFS time-frequency frame, the transformation thereby creating a 2D OTFS time-frequency frame based wave aggregate;

further scrambling the 2D OTFS time-frequency frame based wave aggregate with a scrambling operation;

using a wireless transmitter to modulate and transmit portions of the scrambled 2D OTFS time-frequency frame based wave aggregate, over the plurality of narrow-band subcarriers, over a plurality of time intervals;

wherein a granularity and extent of the portions, the plurality of narrow-band subcarriers, and the time intervals are chosen so that the sum of the transmitted portions accurately characterize the scrambled 2D OTFS time-frequency frame based wave aggregate;

wherein the impaired wireless channel distorts the transmitted portions into channel distorted portions;

using a wireless receiver to receive and demodulate the channel distorted portions over the plurality of narrow-band subcarriers, over a plurality of time intervals, thereby recovering a channel distorted replica of the scrambled 2D OTFS time-frequency frame based wave aggregate;

using an inverse of the scrambling operation to descramble the channel distorted replica of the scrambled 2D OTFS time-frequency frame based wave aggregate, thereby creating a descrambled channel distorted replica of the 2D OTFS time-frequency based wave aggregate;

using at least one processor and an inverse of the OTFS transform to inverse transform the channel distorted replica of the 2D OTFS time-frequency frame based wave aggregate, thereby producing, once substantially all of the portions have been received, a channel distorted replica of the 2D OTFS delay-Doppler frame;

using a delay-Doppler 2D equalizer to correct the channel distorted replica of the 2D OTFS delay-Doppler frame, thereby producing a channel deconvoluted 2D OTFS delay-Doppler frame;

and extracting a plurality of replica data symbols from the channel deconvoluted 2D OTFS delay-Doppler frame.

2. The method of claim 1, wherein the scrambling operation is a null operation, or wherein the scrambling operation is selected to perform at least one of managing peak transmitter power and allowing receivers to distinguish between different transmitters.

3. The method of claim 1, wherein the mutually orthogonal 2D basis wave functions are 2D Fourier or Fourier-like basis functions.

4. The method of claim 1, wherein any of the OTFS transform and the inverse of the OTFS transform are Fourier-like transforms and inverse Fourier-like transforms including transforms selected from the group consisting of symplectic Fourier transforms, symplectic discrete Fourier transforms, symplectic finite Fourier transforms, inverse symplectic Fourier transforms, inverse symplectic discrete Fourier transforms, inverse symplectic finite Fourier transforms, fast Fourier transforms, inverse fast Fourier transforms, wavelet transforms, inverse wavelet transforms, discrete wavelet transforms, and inverse discrete wavelet transforms.

5. The method of claim 1, wherein at least for the transmitter, the 2D OTFS time-frequency frame has a rectangular grid structure and parameters in which the plurality of time intervals is N time intervals, and the plurality of narrow band subcarriers is M subcarriers, each time interval has duration T, and each narrow band subcarrier has frequency bandwidth Δ

f.

6. The method of claim 5, wherein at least for the transmitter, the 2D OTFS delay-Doppler frame comprises N*M locations, and the OTFS transform distributes N*M data symbols over the 2D OTFS time-frequency frame.

7. The method of claim 5, wherein at least for the transmitter, further using any of anticipated wireless time delay and anticipated wireless Doppler shift characteristics of the impaired wireless channel to configure parameters of at least the 2D OTFS delay-Doppler frame.

8. The method of claim 1, wherein the transmitter is an OFDM backward compatible transmitter, the receiver is an OFDM backward compatible receiver, and the plurality of narrow band subcarriers are a plurality of narrow-band OFDM subcarriers.

9. The method of claim 8, wherein the OFDM backward compatible transmitter transmits the portions of the 2D OTFS time-frequency frame based wave aggregates, over the plurality of narrow-band OFDM subcarriers, over the plurality of time intervals, in a manner that is either:

A. compatible with interspersed legacy OFDM symbols originating from other transmitters that are carried over at least some of the plurality of narrow-band OFDM subcarriers and/or over at least some of the time intervals; and

/or

B. compatible with interspersed legacy OFDM symbols originating from the OFDM backward compatible transmitter that are carried over at least some of the plurality of narrow-band OFDM subcarriers and/or over at least some of the time intervals.

10. The method of claim 9, wherein the legacy OFDM symbols comprise 4G/LTE symbols, and at least one of the OFDM backward compatible transmitter or the OFDM backward compatible receiver are configured to operate according to any of OTFS and 4G/LTE methods, or other legacy OFDM method.

11. The method of claim 10, wherein the 4G/LTE symbols are transmitted along with a plurality of OFDM subcarrier and symbol time localized 4G/LTE legacy pilot symbols;

further using the OFDM backward compatible receiver to receive the plurality of legacy 4G/LTE pilot symbols as channel distorted legacy 4G/LTE pilot symbols, and using the channel distorted 4G/LTE pilot symbols to at least partially configure either a delay-Doppler 2D equalizer or a time-frequency 2D equalizer.

12. The method of claim 1, wherein the at least one processor distributes the plurality of data symbols over a plurality of different sized frames by using different sized 2D delay-Doppler frames, thereby creating a plurality of different sized 2D OTFS time-frequency frame based wave aggregates;

further transmitting portions of the different sized 2D OTFS time-frequency frame based wave aggregates, in any of a time or frequency interspersed manner, either within the different sized frames or outside of the different sized frames;

further using the wireless receiver to distinguish, on a different sized frame basis, between channel distorted replicas of the different sized 2D OTFS time-frequency frame based wave aggregates, and to extract the plurality of replica data symbols from appropriate channel deconvoluted different sized 2D delay-Doppler frames.

13. The method of claim 12, wherein at least some of the different sized 2D delay-Doppler frames and corresponding different sized 2D OTFS time-frequency frame based wave aggregates are chosen for at least one of reduced latency, increased rate of data symbol transmission, increased tolerance to channel Doppler shifts and increased tolerance to channel multi-path delay effects.

14. The method of claim 1, wherein at least some of the plurality of data symbols comprise delay-Doppler pilot symbols, further using the at least one processor to distribute at least one delay-Doppler pilot symbol on at least one defined delay-Doppler pilot symbol location, along with the plurality of data symbols, over the 2D delay-Doppler frame;

further transforming the data symbols and the at least one delay-Doppler pilot symbol on the 2D delay-Doppler frame, thereby creating a 2D OTFS time-frequency frame based wave aggregate in a manner that also spreads the at least one delay-Doppler pilot symbol, in a lossless manner, throughout substantially all of the 2D OTFS time-frequency frame based wave aggregate;

wherein during transit from the wireless transmitter to the wireless receiver, the transmitted portions of the 2D OTFS time-frequency frame based wave aggregate are channel distorted according to delay and Doppler characteristics of the channel;

at the receiver, using the at least one processor, knowledge pertaining to the at least one delay-Doppler pilot symbol and at least one defined pilot symbol location, and the channel distortions, to recover a 2D impulse response of the channel, and use the 2D impulse response to configure the delay-Doppler 2D equalizer.

15. The method of claim 14, wherein the delay Doppler 2D equalizer is capable of operation without use of OFDM cyclic prefixes or use of OFDM subcarrier or symbol time localized pilot symbols.

16. The method of claim 1, wherein at least the OTFS time-frequency frame has a non-rectangular grid structure, and the non-rectangular grid structure in turn controls any of start times, time durations, frequencies, frequencies over time, bandwidths, or bandwidths over time of any of the portions, the plurality of time intervals and the plurality of narrow band subcarriers.

17. The method of claim 1, wherein on a per narrow band subcarrier basis, the plurality of time intervals have non-identical start times, such that the transmitter starting time at one subcarrier is not the same as the transmitter starting time at a different subcarrier.

18. The method of claim 1, wherein the receiver comprises both a time-frequency 2D equalizer that operates on the contents of the time-frequency frame, and a delay-Doppler 2D equalizer that operates at the contents of the delay-Doppler frame.

19. The method of claim 18, further using the at least one processor to distribute at least one time-frequency pilot symbol on at least one defined pilot symbol time-frequency location, along with the plurality of data symbols, over at least one defined time and frequency location and portion of a 2D time-frequency frame that is not occupied with the scrambled 2D OTFS time-frequency frame based wave aggregate;

wherein during transit from the wireless transmitter to the wireless receiver, the transmitted at least one time-frequency pilot symbol is also channel distorted according to the delay and Doppler characteristics of the channel;

at the receiver, using the at least one processor, knowledge pertaining to the at least one time-frequency pilot symbol and at least one defined pilot symbol time-frequency location, and the channel distortions, to configure at least the time-frequency 2D equalizer.

20. The method of claim 1, wherein the receiver comprises a plurality of receiver sub-sections, each receiver subsection configured with fractionally different time and frequency offsets, the at least one processor configured to use the receiver subsections to sample the channel distorted replica of the scrambled 2D OTFS time-frequency frame based wave aggregate according to the fractionally different time and frequency offsets, and to combine the samples in a manner that produces a high resolution channel distorted replica of the scrambled 2D OTFS time-frequency frame based wave aggregate over a high resolution version of the receiver'"'"'s 2D OTFS time-frequency frame.

21. The method of claim 20, further comprising one of:

using the high resolution version of the receiver'"'"'s 2D OTFS time-frequency frame to either distinguish between multiple users;

or

further using the high resolution version of the receiver'"'"'s 2D OTFS time-frequency frame with at least one 2D equalizer to further correct for the channel distortions.

56. A wireless communication apparatus comprising a memory and a processor, wherein the memory stores instructions which, when executed by the processor, cause the processor to implement a method recited in any of claims 1 to 55.

22. A method of transmitting, on a per-frame basis, a plurality of data symbols over an impaired wireless channel comprising a plurality of narrow-band subcarriers, the method comprising:

for each frame, using at least one processor to distribute the plurality of data symbols over a 2D OTFS delay-Doppler frame by assigning each data symbol to its own unique 2D OTFS delay-Doppler frame location;

OTFS transforming the data symbols on the 2D OTFS delay-Doppler frame by using each data symbol and frame location to modulate a unique, location specific, 2D basis wave function selected from a set of mutually orthogonal 2D basis wave functions operating over a 2D OTFS time-frequency frame, the transformation also spreading each data symbol, in a lossless and invertible manner, throughout substantially all of the 2D OTFS time-frequency frame, the transformation thereby creating a 2D OTFS time-frequency frame based wave aggregate;

further scrambling the 2D OTFS time-frequency frame based wave aggregate with a scrambling operation; and

using a wireless transmitter to modulate and transmit portions of the scrambled 2D OTFS time-frequency frame based wave aggregate, over the plurality of narrow-band subcarriers, over a plurality of time intervals;

wherein a granularity and extent of the portions, the plurality of narrow-band subcarriers, and the time intervals are chosen so that the sum of the transmitted portions accurately characterize the scrambled 2D OTFS time-frequency frame based wave aggregate;

wherein the impaired wireless channel distorts the transmitted portions into channel distorted portions.

23. The method of claim 22, wherein the scrambling operation is a null operation, or wherein the scrambling operation is selected to perform at least one of managing peak transmitter power and allowing receivers to distinguish between different transmitters.

24. The method of claim 22, wherein the mutually orthogonal 2D basis wave functions are 2D Fourier or Fourier-like basis functions.

25. The method of claim 22, wherein any of the OTFS transform and the inverse of the OTFS transform are Fourier-like transforms and inverse Fourier-like transforms including transforms selected from the group consisting of symplectic Fourier transforms, symplectic discrete Fourier transforms, symplectic finite Fourier transforms, inverse symplectic Fourier transforms, inverse symplectic discrete Fourier transforms, inverse symplectic finite Fourier transforms, fast Fourier transforms, inverse fast Fourier transforms, wavelet transforms, inverse wavelet transforms, discrete wavelet transforms, and inverse discrete wavelet transforms.

26. The method of claim 22, wherein at least for the transmitter, the 2D OTFS time-frequency frame has a rectangular grid structure and parameters in which the plurality of time intervals is N time intervals, and the plurality of narrow band subcarriers is M subcarriers, each time interval has duration T, and each narrow band subcarrier has a frequency bandwidth Δ

f.

27. The method of claim 26, wherein at least for the transmitter, the 2D OTFS delay-Doppler frame comprises N*M locations, and the OTFS transform distributes N*M data symbols over the 2D OTFS time-frequency frame.

28. The method of claim 26, wherein at least for the transmitter, further using any of anticipated wireless time delay and anticipated wireless Doppler shift characteristics of the impaired wireless channel to configure parameters of at least the 2D OTFS delay-Doppler frame.

29. The method of claim 22, wherein the transmitter is an OFDM backward compatible transmitter, and the plurality of narrow band subcarriers are a plurality of narrow-band OFDM subcarriers.

30. The method of claim 29, wherein the OFDM backward compatible transmitter transmits the portions of the 2D OTFS time-frequency frame based wave aggregates, over the plurality of narrow-band OFDM subcarriers, over the plurality of time intervals, in a manner that is either:

A. compatible with interspersed legacy OFDM symbols originating from other transmitters that are carried over at least some of the plurality of narrow-band OFDM subcarriers and/or over at least some of the time intervals; and

/or

B. compatible with interspersed legacy OFDM symbols originating from the OFDM backward compatible transmitter that are carried over at least some of the plurality of narrow-band OFDM subcarriers and/or over at least some of the time intervals.

31. The method of claim 30, wherein the legacy OFDM symbols comprise 4G/LTE symbols, and at least the OFDM backward compatible transmitter operates according to any of OTFS and 4G/LTE methods, or other legacy OFDM method.

32. The method of claim 31, wherein the 4G/LTE symbols are transmitted along with a plurality of OFDM subcarrier and symbol time localized 4G/LTE legacy pilot symbols.

33. The method of claim 22, wherein the at least one processor distributes the plurality of data symbols over a plurality of different sized frames by using different sized 2D delay-Doppler frames, thereby creating a plurality of different sized 2D OTFS time-frequency frame based wave aggregates;

further transmitting portions of the different sized 2D OTFS time-frequency frame based wave aggregates, in any of a time or frequency interspersed manner, either within the different sized frames or outside of the different sized frames.

34. The method of claim 33, wherein at least some of the different sized 2D delay-Doppler frames and corresponding different sized 2D OTFS time-frequency frame based wave aggregates are chosen for at least one of reduced latency, increased rate of data symbol transmission, increased tolerance to channel Doppler shifts and increased tolerance to channel multi-path delay effects.

35. The method of claim 22, wherein at least some of the plurality of data symbols comprise delay-Doppler pilot symbols, further using the at least one processor to distribute at least one delay-Doppler pilot symbol on at least one defined delay-Doppler pilot symbol location, along with the plurality of data symbols, over the 2D delay-Doppler frame;

further transforming the data symbols and the at least one delay-Doppler pilot symbol on the 2D delay-Doppler frame, thereby creating a 2D OTFS time-frequency frame based wave aggregate in a manner that also spreads the at least one delay-Doppler pilot symbol, in a lossless manner, throughout substantially all of the 2D OTFS time-frequency frame based wave aggregate;

wherein during transit from the wireless transmitter to the wireless receiver, the transmitted portions of the 2D OTFS time-frequency frame based wave aggregate are channel distorted according to delay and Doppler characteristics of the channel.

36. The method of claim 35, wherein the delay Doppler 2D equalizer is capable of operation without use of OFDM cyclic prefixes or use of OFDM subcarrier or symbol time localized pilot symbols.

37. The method of claim 22, wherein at least the OTFS time-frequency frame has a non-rectangular grid structure, and the non-rectangular grid structure in turn controls any of start times, time durations, frequencies, frequencies over time, bandwidths, or bandwidths over time of any of the portions, the plurality of time intervals and the plurality of narrow band subcarriers.

38. The method of claim 22, wherein on a per narrow band subcarrier basis, the plurality of time intervals have non-identical start times, such that the transmitter starting time at one subcarrier is not the same as the transmitter starting time at a different subcarrier.

39. The method of claim 38, further using the at least one processor to distribute at least one time-frequency pilot symbol on at least one defined pilot symbol time-frequency location, along with the plurality of data symbols, over at least one defined time and frequency location and portion of a 2D time-frequency frame that is not occupied with the scrambled 2D OTFS time-frequency frame based wave aggregate;

wherein during transit from the wireless transmitter to the wireless receiver, the transmitted at least one time-frequency pilot symbol is also channel distorted according to the delay and Doppler characteristics of the channel.

40. A method of receiving, on a per-frame basis, a plurality of data symbols over an impaired wireless channel comprising a plurality of narrow-band subcarriers, wherein the impaired wireless channel distorts the transmitted portions into channel distorted portions;

the method comprising;

using a wireless receiver to receive and demodulate the channel distorted portions over the plurality of narrow-band subcarriers, over a plurality of time intervals, thereby recovering a channel distorted replica of the scrambled 2D OTFS time-frequency frame based wave aggregate;

using an inverse of the scrambling operation to descramble the channel distorted replica of the scrambled 2D OTFS time-frequency frame based wave aggregate, thereby creating a descrambled channel distorted replica of the 2D OTFS time-frequency based wave aggregate;

using at least one processor and an inverse of the OTFS transform to inverse transform the channel distorted replica of the 2D OTFS time-frequency frame based wave aggregate, thereby producing, once substantially all of the portions have been received, a channel distorted replica of the 2D OTFS delay-Doppler frame;

using a delay-Doppler 2D equalizer to correct the channel distorted replica of the 2D OTFS delay-Doppler frame, thereby producing a channel deconvoluted 2D OTFS delay-Doppler frame; and

extracting a plurality of replica data symbols from the channel deconvoluted 2D OTFS delay-Doppler frame.

41. The method of claim 40, wherein the scrambling operation is a null operation, or wherein the scrambling operation is selected to perform at least one of managing peak transmitter power and allowing receivers to distinguish between different transmitters.

42. The method of claim 40, wherein the mutually orthogonal 2D basis wave functions are 2D Fourier or Fourier-like basis functions.

43. The method of claim 40, wherein any of the OTFS transform and the inverse of the OTFS transform are Fourier-like transforms and inverse Fourier-like transforms including transforms selected from the group consisting of symplectic Fourier transforms, symplectic discrete Fourier transforms, symplectic finite Fourier transforms, inverse symplectic Fourier transforms, inverse symplectic discrete Fourier transforms, inverse symplectic finite Fourier transforms, fast Fourier transforms, inverse fast Fourier transforms, wavelet transforms, inverse wavelet transforms, discrete wavelet transforms, and inverse discrete wavelet transforms.

44. The method of claim 40, wherein at least for the transmitter, the 2D OTFS delay-Doppler frame comprises N*M locations, and the OTFS transform distributes N*M data symbols over the 2D OTFS time-frequency frame.

45. The method of claim 40, wherein the receiver is an OFDM backward compatible receiver.

46. The method of claim 40, wherein the 4G/LTE symbols are transmitted along with a plurality of OFDM subcarrier and symbol time localized 4G/LTE legacy pilot symbols;

further using the OFDM backward compatible receiver to receive the plurality of legacy 4G/LTE pilot symbols as channel distorted legacy 4G/LTE pilot symbols, and using the channel distorted 4G/LTE pilot symbols to at least partially configure either a delay-Doppler 2D equalizer or a time-frequency 2D equalizer.

47. The method of claim 40, wherein the at least one processor distributes the plurality of data symbols over a plurality of different sized frames by using different sized 2D delay-Doppler frames, thereby creating a plurality of different sized 2D OTFS time-frequency frame based wave aggregates;

further using the wireless receiver to distinguish, on a different sized frame basis, between channel distorted replicas of the different sized 2D OTFS time-frequency frame based wave aggregates, and to extract the plurality of replica data symbols from appropriate channel deconvoluted different sized 2D delay-Doppler frames.

48. The method of claim 47, wherein at least some of the different sized 2D delay-Doppler frames and corresponding different sized 2D OTFS time-frequency frame based wave aggregates are chosen for at least one of reduced latency, increased rate of data symbol transmission, increased tolerance to channel Doppler shifts and increased tolerance to channel multi-path delay effects.

49. The method of claim 40, wherein at least some of the plurality of data symbols comprise delay-Doppler pilot symbols, further using the at least one processor to distribute at least one delay-Doppler pilot symbol on at least one defined delay-Doppler pilot symbol location, along with the plurality of data symbols, over the 2D delay-Doppler frame;

at the receiver, using the at least one processor, knowledge pertaining to the at least one delay-Doppler pilot symbol and at least one defined pilot symbol location, and the channel distortions, to recover a 2D impulse response of the channel, and use the 2D impulse response to configure the delay-Doppler 2D equalizer.

50. The method of claim 49, wherein the delay Doppler 2D equalizer is capable of operation without use of OFDM cyclic prefixes or use of OFDM subcarrier or symbol time localized pilot symbols.

51. The method of claim 40, wherein at least the OTFS time-frequency frame has a non-rectangular grid structure, and the non-rectangular grid structure in turn controls any of start times, time durations, frequencies, frequencies over time, bandwidths, or bandwidths over time of any of the portions, the plurality of time intervals and the plurality of narrow band subcarriers.

52. The method of claim 40, wherein the receiver comprises both a time-frequency 2D equalizer that operates on the contents of the time-frequency frame, and a delay-Doppler 2D equalizer that operates at the contents of the delay-Doppler frame.

53. The method of claim 40, further using the at least one processor to distribute at least one time-frequency pilot symbol on at least one defined pilot symbol time-frequency location, along with the plurality of data symbols, over at least one defined time and frequency location and portion of a 2D time-frequency frame that is not occupied with the scrambled 2D OTFS time-frequency frame based wave aggregate;

at the receiver, using the at least one processor, knowledge pertaining to the at least one time-frequency pilot symbol and at least one defined pilot symbol time-frequency location, and the channel distortions, to configure at least the time-frequency 2D equalizer.

54. The method of claim 40, wherein the receiver comprises a plurality of receiver sub-sections, each receiver subsection configured with fractionally different time and frequency offsets, the at least one processor configured to use the receiver subsections to sample the channel distorted replica of the scrambled 2D OTFS time-frequency frame based wave aggregate according to the fractionally different time and frequency offsets, and to combine the samples in a manner that produces a high resolution channel distorted replica of the scrambled 2D OTFS time-frequency frame based wave aggregate over a high resolution version of the receiver'"'"'s 2D OTFS time-frequency frame.

55. The method of claim 54, further comprising one of:

using the high resolution version of the receiver'"'"'s 2D OTFS time-frequency frame to either distinguish between multiple users;

or

further using the high resolution version of the receiver'"'"'s 2D OTFS time-frequency frame with at least one 2D equalizer to further correct for the channel distortions.

57. A system, method or apparatus disclosed herein.