What is claimed is:

1. A method of transmitting data over a communication channel, the method comprising: receiving a plurality of information symbols;

encoding an NxM array containing the plurality of information symbols into a two- dimensional array of modulation symbols by spreading each of the plurality of information symbols with respect to both time and frequency, and

transmitting the two-dimensional array of modulation symbols using M mutually orthogonal waveforms included within M frequency sub-bands.

2 The method of claim 1 wherein the encoding includes:

transforming the NxM array into an array of filtered OFDM symbols using at least one Fourier transform and a filtering process;

transforming the array of filtered OFDM symbols into an array of OTFS symbols using at least one two-dimensional Fourier transform wherein the array of OTFS symbols corresponds to the two-dimensional array of modulation symbols.

3. The method of claim 2 wherein the transmitting includes using a set of M narrow-band filters to produce the M waveforms.

4 T he method of claim 1 wherein the encoding includes combining an inverse symplectic transform with a windowing operation.

5. The method of claim 1 wherein the encoding is performed in accordance with the following relationship:

where x[l, k], k = 0, ... , N— 1, 1 = 0, ... , M— 1 represents the NxM array containing the plurality of information symbols, X[n, m], n = 0, ... , N— 1, m = 0, ... , M— 1 represents the two-dimensional array of modulation symbols, W_{tr} [n, m] is a windowing function, and

represent a set of basis functions.

6. An automated method of wireless communication over a data channel, the method

comprising:

receiving a plurality of data symbols;

encoding an NxM two-dimensional array containing the plurality of data symbols into a two-dimensional array of modulation symbols by spreading each of the plurality of data symbols using a set of cyclically time-shifted and frequency-shifted basis functions; and

transmitting the two-dimensional array of modulation symbols using M mutually orthogonal wireless waveforms included within M frequency sub-bands.

7. The method of claim 6, wherein the encoding includes:

transforming the NxM two-dimensional array of data symbols into an array of filtered OFDM symbols using at least one Fourier transform and a filtering process; and

transforming the array of filtered OFDM symbols into an array of OTFS symbols using at least one two-dimensional Fourier transform wherein the array of OTFS symbols corresponds to the two-dimensional array of modulation symbols.

8. The method of claim 6, wherein said encoding includes:

encoding the NxM two-dimensional array containing the plurality of data symbols onto at least one symplectic-like analysis compatible manifold distributed over a column time axis of length T and row frequency axis of length F, thereby producing at least one Information manifold;

transforming the at least one Information manifold in accordance with a two-dimensional symplectic-like Fourier transform, thereby producing at least one two-dimensional Fourier transformed Information manifold.

9. The method of claim 8, wherein the transmitting includes transmitting each at least one two-dimensional Fourier transformed Information manifold by:

over all frequencies and times of said two-dimensional Fourier transformed Information manifold, selecting a transmitting time slice of duration proportional to Τμ, where μ= 1/N, and passing those frequencies in said two-dimensional Fourier transformed Information manifold corresponding to said transmitting time slice through a bank of at least M different, non-overlapping, narrow-band frequency filters, and transmitting resulting filtered waveforms as a plurality of at least M simultaneously transmitted mutually orthogonal waveforms, over different transmitted time intervals, until an entire two-dimensional Fourier transformed Information manifold has been transmitted.

10. The method of claim 6 further including:

receiving the M mutually orthogonal wireless waveforms;

determining a two-dimensional channel state;

using an inverse of the encoding and the two-dimensional channel state to extract the plurality of data symbols from the M mutually orthogonal wireless waveforms.

11. The method of claim 9, further including receiving each said at least one two-dimensional Fourier transformed Information manifold by:

over at least all frequencies and times of said two-dimensional Fourier transformed Information manifold, using at least one receiver processor to select a receiving time slice that is less than or equal to the duration of the transmitted time intervals, and receiving these channel convoluted waveforms on each said receiving time slice through a receiving bank of at least M different, non-overlapping, narrow-band frequency filters, and receiving said channel-convoluted waveforms over every receiving time slice until an approximation of said two-dimensional Fourier transformed Information manifold has been received;

performing at least one of:

a) using an inverse of said two-dimensional symplectic-like Fourier transform to transform said approximation of said two-dimensional Fourier transformed Information manifold

into an approximation of said at least one received information manifold, and using information pertaining to said two-dimensional channel state to correct said at least one received information manifold for said data channel impairments;

b) using information pertaining to said two-dimensional channel state to correct said approximation of said two-dimensional Fourier transformed Information manifold for said data channel impairments, and using the inverse of said two-dimensional symplectic-like Fourier transform to in turn produce said at least one received information manifold.

12. An automated method of wirelessly communicating data over a data channel, the method comprising:

encoding an NxM two-dimensional array containing a plurality of data symbols onto at least one symplectic analysis compatible manifold distributed over a column time axis of length T and row frequency axis of length F, thereby producing at least one Information manifold; transforming said at least one Information manifold according to a two-dimensional symplectic-like Fourier transform, thereby producing at least one two-dimensional Fourier transformed Information manifold; and

transmitting each at least one two-dimensional Fourier transformed Information manifold by:

over all frequencies and times of said two-dimensional Fourier transformed Information manifold, selecting a transmitting time slice of duration proportional to Τμ, where μ= 1/N, and passing those frequencies in said two-dimensional Fourier transformed Information manifold corresponding to said transmitting time slice through a bank of at least M different, non-overlapping, narrow-band frequency filters, and transmitting resulting filtered waveforms as a plurality of at least M simultaneously transmitted mutually orthogonal waveforms, over different transmitted time intervals, until an entire two-dimensional Fourier transformed Information manifold has been transmitted.

13. The method of claim 12 wherein the data channel includes an impairment impairing said waveforms, said impairment being at least partially describable according to a two-dimensional channel state of said channel, thereby producing channel-convoluted waveforms, the method further including:

receiving each said at least one two-dimensional Fourier transformed Information manifold by:

over at least all frequencies and times of said two-dimensional Fourier transformed Information manifold, using at least one receiver processor to select a receiving time slice that is less than or equal to the duration of the transmitted time intervals, and receiving these channel convoluted waveforms on each said receiving time slice through a receiving bank of at least M different, non-overlapping, narrow-band frequency filters, and receiving said channel-convoluted waveforms over every receiving time slice until an approximation of said two-dimensional Fourier transformed

Information manifold has been received;

performing at least one of:

a) using an inverse of said two-dimensional symplectic-like Fourier transform to transform said approximation of said two-dimensional Fourier transformed Information manifold into an approximation of said at least one received information manifold, and using information pertaining to said two-dimensional channel state to correct said at least one received information manifold for said data channel impairments;

b) using information pertaining to said two-dimensional channel state to correct said approximation of said two-dimensional Fourier transformed Information manifold for said data channel impairments, and using the inverse of said two-dimensional symplectic-like Fourier transform to in turn produce said at least one received

information manifold; and

using said at least one receiver processor to decode and extract said data symbols from said at least one received information manifold.

14. The method of claim 13, further including transforming said at least one NxM two-dimensional array of data according to a spreading operation either prior or after encoding said at least one NxM two-dimensional array of data symbols onto at least one symplectic analysis compatible manifold;

wherein said receiving processor uses an inverse of said spreading operation to decode and extract said data symbols from said at least one received information manifold.

15. The method of claim 14, wherein said spreading operation is convolution with a two-dimensional chirp operation.

16. The method of claim 13, wherein said non-overlapping, narrow-band frequency filters pass frequencies from said at least one two-dimensional Fourier transformed Information manifold

proportional to , where j is the square root of -1, t corresponds to a given time

slice of duration Τμ chosen from said at least one two-dimensional Fourier transformed

Information manifold, and k corresponds to a given row position on said at least one two-dimensional Fourier transformed Information manifold, where k varies between 1 and M.

17. The method of claim 16, wherein

is proportional to 1/T, and T = M/(allowed wireless bandwidth).

18. The method of claim 12, wherein said at least one two-dimensional Fourier transformed Information manifold has overall dimensions ΝΤ_{μ} according to a time axis and M/T according to a frequency axis, and each cell in said at least one two-dimensional Fourier transformed Information manifold has overall dimensions proportional to Τμ according to a time axis and 1/T according to a frequency axis.

19. The method of claim 13, wherein said receiving includes receiving said at least one two-dimensional Fourier transformed Information manifold according to receiving time slices and receiving banks of different, non-overlapping, narrow-band frequency filters that oversamples the corresponding transmitting time slices and transmitting banks of different, non-overlapping, narrow-band frequency filters.

20. The method of claim 12, wherein the transmitting includes transmitting the two-dimensional Fourier transformed Information as either:

1) a plurality of at least M simultaneously transmitted mutually orthogonal waveforms over either different consecutive transmitted time intervals; or

2) a plurality OTFS data or OTFS pilot bursts comprising at least M simultaneously transmitted mutually orthogonal waveform bursts over different transmitted intervals separated by at least one spacer time interval.

21. A communication device, comprising:

a wireless transmitter;

a processor; and

a memory including program code executable by the processor, the program code including code for causing the processor to:

receive a plurality of information symbols;

encode an NxM array containing the plurality of information symbols into a two-dimensional array of modulation symbols by spreading each of the plurality of information symbols with respect to both time and frequency; and

transmit the two-dimensional array of modulation symbols using M mutually orthogonal waveforms included within M frequency sub-bands.

22. The communication device of claim 21wherein the code for causing the processor to encode includes code for causing the processor to:

transform the NxM array into an array of filtered OFDM symbols using at least one Fourier transform and a filtering process;

transform the array of filtered OFDM symbols into an array of OTFS symbols using at least one two-dimensional Fourier transform.

23. The communication device of claim 21 wherein the code for causing the processor to encode includes code for causing the processor to combine an inverse symplectic transform with a windowing operation.

24. A method of receiving data transmitted over a communication channel, the method comprising:

receiving M mutually orthogonal waveforms included within M frequency sub-bands; demodulating the M mutual iy orthogonal waveforms to recover an estimate of a two-dimensional array of OTFS symbols; and

decoding the two-dimensional array of OTFS symbols in order to generate an estimate of an NxM array containing a plurality of information symbols, the NxM! array having been encoded prior to transmission of the data by spreading each of the plurality of information, symbols with respect to both time and frequency.

25. The method of claim 24 wherein the decoding includes transforming the two-dimensional array of OTFS symbols into an array of OFDM symbols using at least one two-dimensional Fourier transform and transforming the array of OFDM symbols into the estimate of the NxM array using at least one inverse Fourier transform.

26. A method of providing a modulated signal useable in a signal transmission system, the method comprising:

performing a two dimensional time-frequency transformation of a data frame including a plurality of information symbols into a plane of time-frequency modulation symbols; and

generating the modulated signal by performing a Heisenberg transform using the plane of time-frequency modulation symbols.

27. The method of claim 26 wherein the performing the two dimensional time-frequency transformation includes performing an inverse time-frequency symplectic transformation and a windowing operation.

28. A method of providing a modulated signal useable in a signal transmission system, the method comprising:

performing a two dimensional time-frequency transformation of a data frame including a plurality of information symbols into a plane of time-frequency modulation symbols; and

generating the modulated signal based upon the plane of time-frequency modulation symbols using an OFDM modulator.

29. The method of claim 28 wherein the performing the two dimensional transformation includes performing an inverse time-frequency symplectic transformation and a windowing operation.

30. A method of providing a modulated signal useable in a signal transmission system, the method comprising:

performing a two dimensional time-frequency transformation of a data frame including a plurality of information symbols into a plane of time-frequency modulation symbols; and

generating the modulated signal based upon the plane of time-frequency modulation symbols using a multicarrier filter bank (MCFB) modulator.

31. The method of claim 30 wherein the performing the two dimensional time-frequency transformation includes performing an inverse time-frequency symplectic transformation and a windowing operation.

32. A transmitter apparatus, the apparatus comprising:

an OTFS pre-processing unit configured to perform a two dimensional time-frequency transformation of a data frame including a plurality of information symbols into a plane of time-frequency modulation symbols; and

an OFDM modulator configured to generate the modulated signal based upon the plane of time-frequency modulation symbols.

33. The transmitter apparatus of claim 32 wherein the two dimensional transformation comprises an inverse time-frequency symplectic transformation and a windowing operation.

34. A transmitter apparatus, the apparatus comprising:

an OTFS pre-processing unit configured to perform a two dimensional time-frequency transformation of a data frame including a plurality of information symbols into a plane of time-frequency modulation symbols; and

a multicarrier filter bank modulator configured to generate the modulated signal based upon the plane of time-frequency modulation symbols.

35. The transmitter apparatus of claim 34 wherein the two dimensional transformation comprises an inverse time-frequency symplectic transformation and a windowing operation.

36. A method of receiving a modulated signal, the method comprising:

receiving a plurality of signal components of the modulated signal;

generating, by performing an OFDM demodulation operation using the plurality of signal components, a plane of estimated time-frequency modulation symbols; and

providing an estimated data frame by performing an inverse of a two dimensional time-frequency transformation with respect to the plane of estimated time-frequency modulation symbols.

37. The method of claim 36 wherein the performing the inverse of the two dimensional time-frequency transformation includes performing a windowing operation and a symplectic Fourier transform.

38. A method of receiving a modulated signal, the method comprising:

receiving a plurality of signal components of the modulated signal;

generating, by performing a MCFB demodulation operation using the plurality of signal components, a plane of estimated time-frequency modulation symbols; and

providing an estimated data frame by performing an inverse of a two dimensional time-frequency transformation with respect to the plane of estimated time-frequency modulation symbols.

39. The method of claim 38 wherein the performing the inverse of the two dimensional time-frequency transformation includes performing a windowing operation and a symplectic Fourier transform.

40. A receiver apparatus, the apparatus comprising:

a receiver front end, the receiver front end being configured to receive a plurality of signal components of a modulated signal;

an OFDM demodulator configured to generate a plane of estimated time-frequency modulation symbols based upon the plurality of signal components; and

an OTFS post-processing unit operative to provide an estimated data frame, the OTFS post-processing unit performing an inverse of a two dimensional time-frequency transformation with respect to the plane of estimated time-frequency modulation symbols.

41. The receiver apparatus of claim 40 wherein the inverse of the two dimensional time-frequency transformation comprises a windowing operation and a symplectic Fourier transform.

42. A receiver apparatus, the apparatus comprising:

a receiver front end, the receiver front end being configured to receive a plurality of signal components of a modulated signal;

a MCFB demodulator configured to generate a plane of estimated time-frequency modulation symbols based upon the plurality of signal components; and

an OTFS post-processing unit operative to provide an estimated data frame, the OTFS post-processing unit performing an inverse of a two dimensional time-frequency transformation with respect to the plane of estimated time-frequency modulation symbols.

43. The receiver apparatus of claim 42 wherein the inverse of the two dimensional time-frequency transformation comprises a windowing operation and a symplectic Fourier transform.