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.

A discrete Fourier transform spread orthogonal time frequency space modulation method comprises the steps of performing DFT preceding processing and delay-Doppler domain mapping processing on the transmit data symbols, OTFS modulator, and performing delay-Doppler domain demapping processing and IDFT decoding processing on a received signal to realize demodulation; compared with the existing waveforms, including OFDM and DFT-s-OFDM, the proposed DFT-s-OTFS can reduce the bit error rate under high Doppler spread and the peak-to-average power ratio of the transmitted signal at the same time.

A pilot reception processing method includes: determining a first position of a pilot pattern corresponding to a pilot in a delay-Doppler domain; and determining first indication information according to the first position.

An access node, user equipment, apparatuses, methods, and computer programs for a communication system. An apparatus for a wireless transmitter device includes a transmitter module for transmitting wireless transmissions and a processing module, which controls the transmitter module. The processing module generates one or more transmit symbols in a Delay-Doppler domain to obtain a Delay-Doppler representation; transforms the Delay-Doppler representation into a Time-Frequency domain to obtain a Time-Frequency representation, the Time-Frequency representation having a first bandwidth and a first duration; adds pilot symbols to the Time-Frequency representation to obtain a Time-Frequency representation with an extended second bandwidth or an extended second duration; transforms the Time-Frequency representation with the extended second bandwidth or the extended second duration to the time domain to obtain a time domain representation; and transmits the time domain representation to a wireless receiver device.

A method for detecting OTFS pilot interference including receiving delay-Doppler-domain samples of a received OTFS delay-Doppler frame, wherein the delay-Doppler domain samples are derived by a two-dimensional symplectic Fourier transformation of time-frequency domain samples resulting from sampling a time-varying received OFTS coded signal; summing the squares of the amplitudes of the delay-Doppler domain samples of the delay-Doppler grid positions evaluated for the channel estimation to establish the received non-interfering pilot power; summing the squares of the amplitudes of all the delay-Doppler domain samples of the complete delay-Doppler grid to establish the total received frame power; comparing a pilot power ratio derived by dividing the non-interfering pilot power by the total received frame power with a guard space ratio derived by dividing the sum of the number of guard and pilot grid spaces in the transmitted OTFS frame by the total number of grid spaces of the transmitted OTFS frame.

A method for user localization in a cellular network includes receiving, by a receiver unit, Orthogonal Time Frequency Space (OTFS) modulated Constant-Amplitude-Zero-Autocorrelation (CAZAC) sequences generated and transmitted in a Doppler-delay domain by a transmitter unit. The method further includes estimating, by the receiver unit, Doppler shift and/or relative speed between the transmitter unit and the receiver unit by filtering the received OTFS modulated CAZAC sequences.

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.

A method for modulating data for transmission within a communication system. The method includes establishing a time-frequency shifting matrix of dimension N×N, wherein N is greater than one. The method further includes combining the time-frequency shifting matrix with a data frame to provide an intermediate data frame. A transformed data matrix is provided by permuting elements of the intermediate data frame. A modulated signal is generated in accordance with elements of the transformed data matrix.

Wireless communication transmission and reception techniques are described. At transmitter, source data bits are modulated into a number Nd of constellation symbols. An invertible transform is applied to the constellation symbols, thereby resulting in mapping the transformed symbols into Nd elements in the time-frequency grid. A signal resulting from the invertible transform is transmitted over a communication channel.