Multimedia codecs (compression methods), based only on FFT (Fast Fourier Transform) have been recently proposed. These codecs use the largest points (foreground) and the most energetic bands (background). Medium quality versions are based on the largest local peaks only.

The phases can be ignored with the largest local peaks or in the background. Alternatively, sine and cosine amplitudes can be used.

This invention describes methods for giving utility to the reintroduced phases, in particular: local peaks are grouped to have a very narrow bandwidth, with the phases containing the displacements of these peaks, and we transport data and the points of the foreground in the phases of the background.

High speed communications are supported using techniques similar to OFDM (Orthogonal Frequency-Division Multiplexing). These processes are intended to be used in particular with connected objects and in the physical layers of computer networks.

Techniques for performing channel estimation in an orthogonal time, frequency and space (OTFS) communication system include receiving a wireless signal comprising a data signal portion and a pilot signal portion in which the pilot signal portion includes multiple pilot signals multiplexed together in the OTFS domain, performing two-dimensional channel estimation in a time-frequency domain based on a minimum mean square error (MMSE) optimization criterion, and recovering information bits using a channel estimate obtained from the two-dimensional channel estimation.

Orthogonal Time Frequency Space (OTFS) is a novel modulation scheme with significant benefits for 5G systems. The fundamental theory behind OTFS is presented in this paper as well as its benefits. We start with a mathematical description of the doubly fading delay-Doppler channel and develop a modulation that is tailored to this channel. We model the time varying delay-Doppler channel in the time-frequency domain and derive a new domain (the OTFS domain) where we show that the channel is transformed to a time invariant one and all symbols see the same SNR. We explore aspects of the modulation like delay and Doppler resolution, and address design and implementation issues like multiplexing multiple users and evaluating complexity. Finally we present some performance results where we demonstrate the superiority of OTFS.

Apparatuses, methods, and systems are disclosed for precoding wireless communications. An apparatus includes a processor that determines a transform precoder. The processor (805) precodes a plurality of source information symbols over a set of available physical transmission resources using the determined transform precoder. The processor combines the precoded source information symbols using a redundant representation.

Method and apparatus for PTRS for OTFS waveforms. The apparatus measures a PTRS using an OTFS including a delay-Doppler domain. The OTFS includes a plurality of symbols in the delay-Doppler domain based on the PTRS. A first symbol of the plurality of symbols includes a first PTRS resource sample having a first value in the delay-Doppler domain. A second symbol of the plurality of symbols includes a second PTRS resource sample having a second value in the delay-Doppler domain. The first PTRS resource sample is adjacent to the second PTRS resource sample. The apparatus performs phase noise tracking for a data channel based on the measured PTRS.

Systems and methods for transmitting data using various Modulation on Zeros schemes are described. In many embodiments, a communication system is utilized that includes a transmitter having a modulator that modulates a plurality of information bits to encode the bits in the zeros of the z-transform of a discrete-time baseband signal. In addition, the communication system includes a receiver having a decoder configured to decode a plurality of bits of information from the samples of a received signal by: determining a plurality of zeros of a z-transform of a received discrete-time baseband signal based upon samples from a received continuous-time signal, identifying zeros that encode the plurality of information bits, and outputting a plurality of decoded information bits based upon the identified zeros.

Various embodiments of this disclosure relate to generation and reception of signals comprising cyclically shifted basis functions. A device may obtain a set of modulation symbols and modulate a plurality of basis functions based on the set of modulation symbols to generate a signal. The plurality of basis functions may comprise cyclically shifted versions of a basis function and a periodic autocorrelation function of the basis function may comprise an ideal (e.g., perfect) periodic autocorrelation function.

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.

Methods, systems and device for achieving synchronization in an orthogonal time frequency space (OTFS) signal receiver are described. An exemplary signal reception technique includes receiving an OTFS modulated wireless signal comprising pilot signal transmissions interspersed with data transmissions, calculating autocorrelation of the wireless signal using the wireless signal and a delayed version of the wireless signal that is delayed by a pre-determined delay, thereby generating an autocorrelation output, processing the autocorrelation filter through a moving average filter to produce a fine timing signal. Another exemplary signal reception technique includes receiving an OTFS modulated wireless signal comprising pilot signal transmissions interspersed with data transmissions, performing an initial automatic gain correction of the received OTFS wireless signal by peak detection and using clipping information, performing coarse automatic gain correction on results of a received and initial automatic gain control (AGC)-corrected signal.

Embodiments of this application provide a communication method. The method includes: generating a first reference signal, where the first reference signal is two-dimensional orthogonal to a second reference signal, the second reference signal is a reference signal obtained after delay τ transform and Doppler frequency shift ν transform are performed on the first reference signal in a communication process, 0≤τ≤τ.sub.max, 0≤|ν|≤ν.sub.max, τ≠0 or ν≠0,τ.sub.max is a first threshold, ν.sub.max is a second threshold, and |x| represents an absolute value of x; and transmitting the first reference signal.