Systems and methods for symplectic orthogonal time frequency shifting modulation and transmission of data

An automated method of wirelessly transmitting and receiving data over an impaired data channel connecting at least one wireless transmitter and at least one wireless receiver, said data comprising a plurality of data symbols, said method comprising:

• using at least one transmitter processor to package said data into at least one N×M 2D array of data symbols, and further encoding said at least one N×M 2D array 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;
• using at least one transmitter processor to transform said at least one Information manifold according to a 2D symplectic-like Fourier transform, thereby producing at least one 2D Fourier transformed Information manifold;
• transmitting each at least one 2D Fourier transformed Information manifold by:
• over
• all frequencies and times of said 2D Fourier transformed Information manifold, selecting a transmitting time slice of duration proportional to Tμ, where μ=1/N, and passing those frequencies in said 2D 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 2D Fourier transformed Information manifold has been transmitted:
• wherein said impaired data channel impairs said waveforms, said impairment being at least partially describable according to a 2D channel state of said channel, thereby producing channel-convoluted waveforms at said at least one wireless receiver;
• receiving each said at least one 2D Fourier transformed Information manifold by:
• over at least all frequencies and times of said 2D 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 2D Fourier transformed Information manifold has been received;
• performing at least one of:
• a) using an inverse of said 2D symplectic-like Fourier transform to transform said approximation of said 2D Fourier transformed Information manifold into an approximation of said at least one received information manifold, and using information pertaining to said 2D channel state to correct said at least one received information manifold for said data channel impairments;
• b) using information pertaining to said 2D channel state to correct said approximation of said 2D Fourier transformed Information manifold for said data channel impairments, and using the inverse of said 2D 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.

A wireless communication apparatus, comprising:

• a memory that stores instructions;
• a processor;
• and a radio frequency (RF) transmitter;
• wherein the processor reads instructions from the memory and implements an automated method of wirelessly transmitting data over an impaired data channel, communicatively connecting the RF transmitter and at least one wireless receiver, said data comprising a plurality of data symbols, the instructions comprising:
• instructions for packaging said data into at least one N×M 2D array of data symbols, and further encoding said at least one N×M 2D array 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;
• instructions for transforming said at least one Information manifold according to a 2D symplectic-like Fourier transform, thereby producing at least one 2D Fourier transformed Information manifold;
• instructions for causing the RF transmitter to transmit each at least one 2D Fourier transformed Information manifold by:
• over all frequencies and times of said 2D Fourier transformed Information manifold,
• instructions for selecting a transmitting time slice of duration proportional to Tμ, where μ=1/N, and passing those frequencies in said 2D 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 2D Fourier transformed Information manifold has been transmitted;
• wherein said impaired data channel impairs said waveforms, said impairment being at least partially describable according to a 2D channel state of said channel, thereby producing channel-convoluted waveforms at said at least one wireless receiver.