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.

Abstract: An alternative method of data communications using orthogonal time frequency shifting (OTFS) wireless waveforms configured so as to transmit data in a manner that is relatively insensitive to communications channel distortions and frequency shifts. In contrast to prior methods taught by applicant, the present disclosure teaches an alternative modulation scheme that maps data symbols intended for data transmission onto a symplectic-like 2D Fourier transform which operates on a form of the original data symbols. This 2D Fourier transform in turn is passed through a filter bank of narrow band filters, and the output in turn used to modulate transmitted waveforms according to various time slices until the entire 2D Fourier transform has been transmitted. At the receiver, and inverse of this process can be used to both characterize the data channel and correct the received signals for channel distortions, thus receiving a clear form of the original data symbols.