Abstract: 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.

Abstract: 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.

Abstract: A fixed wireless access system is implemented using orthogonal time frequency space multiplexing (OTFS). Data transmissions to/from different devices share transmission resources using—delay Doppler multiplexing, time-frequency multiplexing, multiplexing at stream and/or layer level, and angular multiplexing. Time-frequency multiplexing is achieved by dividing the time-frequency plan into subgrids, with the subsampled time frequency grid being used to carry the OTFS data. Antenna implementations include a hemispherical antenna with multiple antenna elements arranged in an array to achieve multiplexing.

Abstract: A wireless communication method includes receiving, by a first wireless device during a training phase, reference tones using a first number of resource elements from a transmitter of a second wireless device, wherein the first wireless device comprises multiple receiving antennas, estimating, by the first wireless device, from the receiving the reference tones, a second order statistics of wireless channels between the multiple receiving antennas and the transmitter of the second wireless device, and performing channel estimation, during an operational phase subsequent to the training phase, using the second order statistics and reference tones received on a second number of resource elements, wherein the second number is less than the first number.

Abstract: A method for performing downlink transmissions from a transmitting device to multiple user devices using transmission resources from a multi-dimensional grid of resources is described. The method includes logically partitioning the transmission resources into multiple segments, assigning, to a given user device of the multiple user devices, transmission resources of one or more of the multiple segments, and performing, using at least some of the assigned transmission resources for the given user device, a downlink transmission using an orthogonal time frequency space (OTFS) transformation on data or signals to be transmitted to the given user device.

Abstract: A method of reducing peak to average power ratio of uplink transmission includes, assigning a slice of transmission resource to uplink transmission from a user equipment, where all resource elements in the slice have a same Doppler value, mapping data to the slice, performing orthogonal time frequency space transformation to generate time-frequency domain data and processing the time-frequency domain data for transmission.

Abstract: Fiber, cable, and wireless data channels are typically impaired by reflectors and other imperfections, producing a channel state with echoes and frequency shifts in data waveforms. Here, methods of using OTFS pilot symbol waveform bursts to automatically produce a detailed 2D model of the channel state are presented. This 2D channel state can then be used to, optimize data transmission. For wireless data channels, an even more detailed 2D model of channel state can be produced by using polarization and multiple antennas in the process. Once 2D channel states are known, the system turns imperfect data channels from a liability to an advantage by using channel imperfections to boost data transmission rates. The methods can be used to improve legacy data transmission modes in multiple types of media, and are particularly useful for producing new types of robust and high capacity wireless communications using non-legacy OTFS data transmission methods.

Abstract: In a transmitter apparatus, a known reference signal is superimposed on top of a data signal that is typically not known a priori to a receiver and the combined signal is transmitted. At a receiver, an iterative channel estimation and equalization technique is used to recover the reference signal and the unknown data signal. In the initial iteration, the known reference signal is recovered by treating the data signal as noise. Subsequent iterations are used to improve estimation of received reference signal and the unknown data signal.

Abstract: A system and method for orthogonal time frequency space communication and waveform generation. The method includes receiving a plurality of information symbols and encoding an N×M 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. The two-dimensional array of modulation symbols is then transmitted using M mutually orthogonal waveforms included within M frequency sub-bands.

Abstract: A method for performing downlink transmissions from a transmitting device to multiple user devices using transmission resources from a multi-dimensional grid of resources is described. The method includes logically partitioning the transmission resources into multiple segments, assigning, to a given user device of the multiple user devices, transmission resources of one or more of the multiple segments, and performing, using at least some of the assigned transmission resources for the given user device, a downlink transmission using an orthogonal time frequency space (OTFS) transformation on data or signals to be transmitted to the given user device.

Abstract: 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.

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: Inconspicuous antenna systems configured to include substantially transparent conducting and dielectric materials or open lattice structures. The antenna systems are capable of distinguishing wireless waveforms over a plurality of different polarization states and directions. Polarized antenna elements are assembled into antenna sets, each set with a different directionality. The different directionality sets in turn form the antenna system. Directionality can be achieved by employing different printed antenna like designs, variable length microstrips, Rotman lenses, active phase adjust, metamaterials, and other methods. The antenna system can be widely used in urban environments and installed as visually inconspicuous retrofits over building windows, street lights, air conditioning units, and the like.

Abstract: Methods, systems and devices for lattice reduction in decision feedback equalizers for orthogonal time frequency space (OTFS) modulation are described. An exemplary wireless communication method, implementable by a wireless communication receiver apparatus, includes receiving a signal comprising information bits modulated using OTFS modulation scheme. Each delay-Doppler bin in the signal is modulated using a quadrature amplitude modulation (QAM) mapping. The method also includes estimating the information bits based on an inverse of a single error covariance matrix of the signal, with the single error covariance matrix being representative of an estimation error for all delay-Doppler bins in the signal.

Abstract: A wireless communication method for transmitting wireless signals from a transmitter includes receiving information bits for transmission, segmenting the information bits into a stream of segments, applying a corresponding forward error correction (FEC) code and an interleaver to each of the stream of segments and combining outputs of the interleaving to generate a stream of symbols, processing the stream of symbols to generate a waveform, and transmitting the waveform over a communication medium.

Abstract: Methods, systems and devices for providing transmission resources that achieve transmission diversity while reducing pilot signal overhead are described. An exemplary wireless communication method may be implemented in a wireless communication system in which transmission resources are allocated on a per physical resource block (PRB) basis, where a PRB corresponds to a two dimensional resource pattern comprising a first number of subcarriers along a frequency dimension and a second number time slots along a time dimension. The method includes logically dividing subcarriers in each PRB into an integer number of sub-groups of subcarriers, wherein the integer number is greater than one, allocating, to a transmission, transmission resources corresponding to one or more of the sub-groups of subcarriers, performing the transmission in the wireless communication system.

Abstract: Wireless communication techniques for transmitting and receiving reference signals is described. The reference signals may include pilot signals that are transmitted using transmission resources that are separate from data transmission resources. Pilot signals are continuously transmitted from a base station to user equipment being served. Pilot signals are generated from delay-Doppler domain signals that are processed to obtain time-frequency signals that occupy a two-dimensional lattice in the time frequency domain that is non-overlapping with a lattice corresponding to data signal transmissions.

Abstract: In a transmitter apparatus, a known reference signal is superimposed on top of a data signal that is typically not known a priori to a receiver and the combined signal is transmitted. At a receiver, an iterative channel estimation and equalization technique is used to recover the reference signal and the unknown data signal. In the initial iteration, the known reference signal is recovered by treating the data signal as noise. Subsequent iterations are used to improve estimation of received reference signal and the unknown data signal.

Abstract: Methods, systems and devices for forward error correction in orthogonal time frequency space (OTFS) communication systems using non-binary low-density parity-check (NB-LDPC) codes are described. One exemplary method for forward error correction includes receiving data, encoding the data via a non-binary low density parity check (NB-LDPC) code, wherein the NB-LDPC code is characterized by a matrix with binary and non-binary entries, modulating the encoded data to generate a signal, and transmitting the signal. Another exemplary method for forward error correction includes receiving a signal, demodulating the received signal to produce data, decoding the data via a NB-LDPC code, wherein the NB-LDPC code is characterized by a matrix with binary and non-binary entries, and providing the decoded data to a data sink.

Abstract: A wireless data transmission technique includes encoding information bits as a periodic sequence of quadrature amplitude modulation (QAM) symbols, convolving the periodic sequence with a periodic pulse function, thereby generating a filtered periodic sequence, transforming the filtered periodic sequence to a delay-Doppler domain waveform, converting the delay-Doppler domain waveform to a time domain waveform, and transmitting the time domain waveform.