Orthogonal time frequency space signal communication using predefined basis signals

Abstract

Methods and systems for orthogonal time frequency space (OTFS) communication using predefined basis signals are described. An example digital communication method includes receiving a signal over a communication channel, determining an estimate of the communication channel from one or more pilot symbols in the signal transmission. Herein the one or more pilot symbols are assigned along a delay-Doppler resource grid. The method further includes equalizing non-pilot symbols in the signal transmission by rotating the estimate of the communication channel according to grid locations of the one or more pilot symbols along the delay-Doppler resource grid at other grid locations, and recovering data bits from the equalized non-pilot symbols.

Description

PCT Patent Application 119314.8090.WO00 ORTHOGONAL TIME FREQUENCY SPACE SIGNAL COMMUNICATION USING PREDEFINED BASIS SIGNALS CROSS-REFERENCE TO RELATED APPLICATION

[0001] This patent document claims priority to U.S. Provisional Patent Application No. 63 / 487,725, filed on March 1, 2023, the disclosure of which is hereby incorporated by reference herein in its entirety. TECHNICAL FIELD

[0002] The present document relates to digital communication, and more particularly, to data modulation schemes used for digital communication in wireless systems. BACKGROUND

[0003] Due to an explosive growth in the number of wireless user devices and the amount of wireless data that these devices can generate or consume, current wireless communication networks are fast running out of bandwidth to accommodate such a high growth in data traffic and provide high quality of service to users.

[0004] Various efforts are underway in the telecommunication industry to come up with next generation of wireless technologies that can keep up with the demand on performance of wireless devices and networks. Many of those activities involve situations in which a large number of user devices may be served by a network. SUMMARY

[0005] This document discloses techniques that may be used by wireless networks to achieve several operational improvements. In particular, a method of generating a waveform called Orthogonal-Time-Frequency-Space (OTFS) is disclosed. For example, an OTFS waveform may be generated using pre-defined basis signals called Pulsones™.

[0006] In one example aspect, a digital communication method is disclosed. The method includes receiving a signal over a communication channel, and determining an estimate of the communication channel from one or more pilot symbols in the signal. In this example, the one or more pilot symbols are assigned along a delay-Doppler resource grid. The method further includes equalizing one or more non-pilot symbols in the signal by rotating the estimate of the communication channel according to grid locations of the one or more pilot symbols along the 165524628.2PCT Patent Application 119314.8090.WO00 delay-Doppler resource grid at other grid locations, and recovering data bits from one or more equalized non-pilot symbols.

[0007] In another example aspect, another digital communication method is disclosed. The method includes generating a signal comprising one or more pilot symbols and one or more non-pilot symbols having transmission resources assigned along a delay-Doppler resource grid, and transmitting the signal over a communication channel. In this example, the one or more pilot symbols are configured to enable (a) a determination of an estimate of the communication channel at a receiver, and (b) a recovery of data bits from the one or more non-pilot symbols by rotating the estimate of the communication channel based on grid locations of the one or more pilot symbols along the delay-Doppler resource grid at other grid locations.

[0008] In another example aspect, a wireless communication apparatus that implements the above-described methods is disclosed. The wireless communication apparatus may include a transmitter circuit and / or a receiver circuit to perform signal transmissions or receptions and a processor to implement various signal processing techniques described in the present document.

[0009] In yet another example aspect, a wireless system in which one or more of the above- described methods are implemented is disclosed.

[0010] In yet another example aspect, the method may be embodied as processor-executable code and may be stored on a computer-readable program medium.

[0011] These, and other, features are described in this document. DESCRIPTION OF THE DRAWINGS

[0012] FIG.1 shows an example communication network.

[0013] FIG.2 shows a simplified example of a wireless communication system in which uplink and downlink transmissions are performed.

[0014] FIG.3 is a block diagram of an example of a transmitter.

[0015] FIG.4 is a block diagram of an embodiment of signal generation.

[0016] FIG.5 is a block diagram of another embodiment of signal generation.

[0017] FIG.6 is a block diagram of yet another embodiment of signal generation.

[0018] FIG.7 is a block diagram of an example implementation.

[0019] FIG.8 shows an example of a hardware platform.

[0020] FIGS.9 and 10 are flowcharts for various example methods of digital communication.

[0021] FIG.11 shows examples of fully and partially overlapping OTFS frames. 165524628.2PCT Patent Application 119314.8090.WO00

[0022] FIG.12 shows an example of multiple OTFS frames with intervening synchronization signals (SS).

[0023] FIGS.13A and 13B show implementation examples of generation of OTFS waveforms that include synchronization signals.

[0024] FIG.14 depicts an example of an iterative decoder in which a single forward error correction (FEC) code is processed.

[0025] FIG.15 shows a block diagram of an example iterative receiver apparatus.

[0026] FIG.16 shows an example of an iterative decoder architecture when using a multi-level- coding (MLC) FEC code.

[0027] FIG.17 shows a block diagram of an example iterative receiver apparatus that uses multi-level decoding. DETAILED DESCRIPTION

[0028] To make the purposes, technical solutions and advantages of this disclosure more apparent, various embodiments are described in detail below with reference to the drawings. Unless otherwise noted, embodiments and features in embodiments of the present document may be combined with each other.

[0029] Section headings are used in the present document to improve readability of the description and do not in any way limit the discussion or the embodiments to the respective sections only. Furthermore, certain standard-specific terms are used for illustrative purpose only, and the disclosed techniques are applicable to any wireless communication systems.

[0030] 1. Examples of the Wireless Communication Environment

[0031] The wireless or time-variant nature of the communication channel poses several challenges in design a transmission protocol suitable for wireless communication scenarios. These days, users expect their wireless devices to work everywhere and in a variety of mobile or stationary situations.

[0032] The relative movement of transmitters and receivers with respect to each other cause signal distortions such as varying channel delay, Doppler and / or angular spread, signal degradation due to ground clutter, sea clutter, and so on. Another example of signal degradation is flat fading in which an entire channel occupied by a transmission signal will experience fading or attenuation that may be relatively constant across the channel. In practice, a transmission scheme may need to be designed to fit within a certain link budget, maximum power constraint, or linearity of electronics used for transmitting or receiving signals.

[0033] 2. Example Wireless Systems 165524628.2PCT Patent Application 119314.8090.WO00

[0034] FIG.1 shows an example of a wireless communication system 100 in which a transmitter device 102 transmits signals to a receiver 104. The signals may undergo various wireless channels and multipaths, as depicted. Some reflectors such as buildings and trees may be static, while others such as cars, may be moving scatterers. The transmitter device 102 may be, for example, a user device, a mobile phone, a tablet, a computer, or another Internet of Things (IoT) device such as a smartwatch, a camera, and so on. The receiver device 104 may be a network device such as the base station. The signals transmitted from the base station to the transmitter 102 may experience similar channel degradations produced by static or moving scatterers. The techniques described in the present document may be implemented by the devices in the wireless communication system 100. The terms “transmitter” and “receiver” are simply used for convenience of explanation. As further described herein, depending on the direction of transmission (uplink or downlink), the network station may be transmitting or receiving and user device may be receiving or transmitting.

[0035] FIG.2 shows a simplified wireless network to highlight certain aspects of the disclosed technology. A transmitter transmits wireless signals to a receiver in the wireless network. Some transmissions in the network, variously called as downlink or downstream transmissions, a network-side node such as a base station acts as a transmitter of wireless signals and one or more user devices act as the receiver of these wireless signals. For some other transmissions, as depicted in FIG.2, the direction of transmission may be reversed. Such transmissions are often called uplink or upstream transmissions. For such transmissions, one or more user devices act as transmitters of the wireless signals and a network-side node such as the base station acts as the receiver of these signals (as depicted in FIG.2). Other type of transmissions in the network may include device-to-device transmissions, sometimes called direct or sideband transmissions. While the present document primarily uses the terms “downlink” and “uplink” for the sake of convenience, similar techniques may also be used for other situations in which transmissions in two directions are performed - e.g., inbound or incoming transmissions that are received by a wireless device and outbound or outgoing transmissions that are transmitted by a wireless device. For example, downlink transmissions may be inbound transmissions for a user device, while outbound transmissions for a network device. Similarly, uplink transmission may be inbound transmissions for a network device while outbound transmissions from a wireless device. Therefore, for some embodiments, the disclosed techniques may also be described using terms such as “inbound” and “outbound” transmission without importing any 3GPP- specific or other wireless protocol-specific meaning to the terms “uplink” and “downlink.” 165524628.2PCT Patent Application 119314.8090.WO00

[0036] In frequency division multiplexing (FDM) networks, the transmissions to a base station and the transmissions from the base station may occupy different frequency bands (each of which may occupy continuous or discontinuous spectrum). In time division multiplexing (TDM) networks, the transmissions to a base station and the transmissions from the base station occupy a same frequency band but are separated in time domain using a TDM mechanism such as time slot-based transmissions.

[0037] 3. OTFS Waveform Overview

[0038] The OTFS waveform is constructed from symbols assigned to a grid in a two- dimensional domain called the delay-Doppler. The grid is characterized by a Doppler period ^^^, typically satisfying ^^^^ 2 ∙ ^^ௗ, where ^^ௗis the maximum expected Doppler shift, and a delay period, ^^^ൌ 1 / ^^^. The grid has ^^ ^ ^ ^^^∙ ^^^ elements along Doppler and ^^ ^ ^ ^^^∙ ^^ ^^^ elements along delay, where ^^ ^^ of the OTFS signal and ^^ is its duration. Ontop of the information bearing quadrature amplitude modulation QAM), the grid may include pilot symbols used for channel detection and estimation.

[0039] The OTFS waveform in the time domain, may be considered to be a super-position of Pulsones™ multiplied by the grid elements ேି^ெି^^^^^^^ൌ ^ ^ ^^^^^, ^^^∙ ^^^^,^^^^^^ (1)

[0040] where ^^^^^, ^^^are^ ^^^^,^^^ ^^^ ≜ ^^ఛ^ ^^^ ∗ ^ ^^௧^ ^^^ ∙ ^ ^^^ଶగ^∆ఔ^ఛ^^^൫ ^^ െ ^^Δ ^^ െ ^^ ^^^൯൩ (2)

[0041] operation, ^^௧^^^^ൌ ℱି^^^^ఔ^is the inverse Fourier transform of a pulse in the Doppler domain,Δ ^^ ൌ ^^^ / ^^ and ∆ ^^ ൌ ^^^ / ^^are the delay and Doppler grid resolutions, respectively, and ^^^∙^ is the Dirac delta function. In general, the Pulsones™ may be considered to be basis signals used for the delay-Doppler grid.

[0042] In this document, we will use the notation ∆^^,^^^^^^^for the second term of (2), which represents an infinite delta train, with rotatingby a time window: ^ ^ ^^^ ^^^ ^ ^^^ଶగ^∆ఔ^ఛ^^^ ^^ ^^ (3)

[0043] Into the effective duration of the time window ^^௧. 165524628.2PCT Patent Application 119314.8090.WO00

[0044] 3.1 Example Implementations using Zak Theory

[0045] In signal processing, it is traditional to represent signals (or waveforms) either in time or in the frequency domain. Each representation reveals different attributes of the signal. The dictionary between these two realizations is the Fourier transform:

[0046] Interestingly, there is another domain where signals can be naturally realized. This domain is called the delay Doppler domain. For the purpose of the present discussion, this is also referred to as the Zak domain. In its simplest form, a Zak signal is a function of two variables. The variable is called delay and the variable is called Doppler. The function is assumed to be periodic along with period and quasi-periodic along with . The quasi periodicity condition is given by:satisfy the Nyquist condition • = 1. Zak domain signalsto time and frequency domain signals throughtransforms and called the time and frequency Zak transforms. In more precise terms, denoting space of Zak signals by , the time and frequency Zak transforms are linear transformations:of the Fourier transform FT = . This factorization isreferred to as the Zak factorization. The Zakembodies the combinatorics of the fast Fourier transform algorithm. Said another way, Zak transforms are principally geometric projections: the time Zak transform is integration along the Doppler variable and reciprocally the frequency Zak transform is integration along the delay variable.

[0049] We next proceed to give the outline of the OTFS modulation. The key thing to note is that the Zak transform plays for OTFS the same role the Fourier transform plays for OFDM. More specifically, in OTFS, the information bits are encoded on the delay Doppler domain as a Zak signal and transmitted through the rule:165524628.2PCT Patent Application 119314.8090.WO00

[0050] where stands for two-dimensional filtering operation with a 2D pulse called twisted convolution (to be explained in the present to the physical time domain is done using the Zak transform.with the analogue formulas in case of frequency division multiple access FDMA and time division multiple access TDMA. In FDMA, the information bits are encoded on the frequency domain as a signal x(f) and transmitted through the rule:

[0051] where the filtering is done on the frequency domain by linear convolution with a 1D pulse w(f) (in case of standard OFDM w(f) is equal an sinc function). The modulation mapping is the Fourier transform. In TDMA, the information bits are encoded on the time domain as a signal x(t) and transmitted through the rule:

[0052] where the filtering is done on the time domain by linear convolution with a 1D pulse w(t). The modulation mapping in this case is identity.

[0053] 3.2 Example Implementations based on Realization Theory

[0054] In some embodiments, the OTFS transceiver can be mathematically interpreted from the point of view of realization theory. In a nutshell, in this approach one considers the signal space of waveforms as a representation space of the Heisenberg group or equivalently as a Hilbert space equipped with collection of Heisenberg operators, each associated with a different point in the delay Doppler plane. This representation space admits multitude of realizations. The two standard ones are the time and frequency realizations and they are related through the one- dimensional Fourier transform. In communication theory the TDMA transceiver structure is naturally adapted to the time realization as QAM symbols are multiplexed along the time coordinate while the OFDM transceiver structure is naturally adapted to the frequency realization as the QAM symbols are multiplexed along the frequency coordinate. The main observation is that, there is a canonical realization lying in between the time and frequency realizations, called the Zak realization. Interestingly, waveforms in Zak realization are represented as functions on a two-dimensional delay Doppler domain satisfying certain quasi- periodicity condition. The main message of this note is that the Zak realization is naturally adapted to the OTFS transceiver. Viewing the OTFS transceiver from this perspective extenuates its novel and independent standing among the other existing transceiver structures.

[0055] 3.3 Example Implementations using Delay-Doppler Lattices 165524628.2PCT Patent Application 119314.8090.WO00

[0056] A delay Doppler lattice is an integral span of a pair of linear independent vectors . In more details, given such a pair, the associated lattice is the set: The vectors are called the lattice basis vectors. It is convenient to arrange thebasis vectors as the first and second columns of a matrix , i.e.,: the lattice , that is, the image of thestandard lattice under the matrix G. The volume of the lattice is by definition the area of the fundamental domain which is equal to the absolute value of the determinant of G. Every lattice admits a symplectic reciprocal lattice, aka orthogonal complement lattice that we denote by . The definition of is:

[0059] We say that is under-sampled if . we say that is critically sampled if . Alternatively, an under-sampled lattice isthat the volume of its fundamental domain is > 1. From this point on we consider only under-sampled lattices. Given a lattice , we define its maximal rectangular sub-lattice as = where:

[0060] When either or ,. We say a lattice is rectangular if .a sub-lattice of a rectangular lattice is also rectangular. A rectangular lattice is under-sampled if > 1. The standard example of a critically sampled rectangular lattice is = ,by the unit matrix:lattice that is not rectangular is the hexagonal lattice Λ୦^^, which is generated by the basis matrix:165524628.2PCT Patent Application 119314.8090.WO00

[0062] where ^^ ൌ^2 / √3. The interesting attribute of the hexagonal lattice is that among all critically sampled lattices it has the longest distance between neighboring points. The maximal rectangular sub-lattice of Λ୦^^is generated by ^^^and 2 ^^ଶെ ^^^.

[0063] In some embodiments, an OTFS transceiver structure depends on the choice of the following parameters: a critically sampled lattice , a filter function and an information grid specified by . We assume that the filter functionwhere the delay and Doppler factors are square root Nyquist with to respectively. We encode the information bits as a periodic 2D with periods (N, M). Multiplying by thestandard Zak signal P we obtain a Zak P. A concrete way to think of P is as theunique quasi periodic extension of the finite sequence where n = 0, .., N–1 and m = 0, .., M–1. We define the modulated transmitproceeds in three steps. In thefirst step the information block is quasi-periodized thus transformed into a discrete Zak signal. In the second step, the bandwidth and duration of the signal are shaped through a 2D filtering procedure defined by twisted convolution with the pulse w. In the third step, the filtered signal is transformed to the time domain through application of the Zak transform. To better understand the structure of the transmit waveform we apply few simple algebraic manipulations to (3.1). First, we note that, being an intertwiner, the Zak transform obeys the relation:can be expressed as twisted convolution .can write:

[0066] where in time. We refer to thewaveform OTFS waveform. We see from Formula (3.3) that the transmitfrom the bare waveform through windowing in time followed by convolution with a pulse. This cascade of operations is the time representation of 2D filtering in 165524628.2PCT Patent Application 119314.8090.WO00 the Zak domain. It is beneficial to study the structure of the bare OTFS waveform in the case is supported on a single grid point (aka consists of a single QAM symbol), i.e., . In this case, one can show that the bare waveform takes the form:infinite delta pulse train ofpulse rate where the shift is determined by the delay parameter n and the modulation is Doppler parameter m. With regard to the de-modulation mapping, given a received waveform ^^୰^, its de-modulated image is defined through the rule:. We oftenincorporate an additional step of sampling and ..

[0069] 4. OTFS Transmitter

[0070] In some embodiments, the OTFS transmitter encodes information bits in one or more Forward-Error-Correction (FEC) codes, corresponding to one or more symbol constellation levels (denoted by ^^), interleave the coded bits and map them to symbols (typically QAM) which are then assigned to delay-Doppler grid elements. Some of the delay-Doppler grid elements may not be assigned with any symbols (value of zero) and others may be assigned with known symbols (pilots). Finally, the OTFS modulator is applied to the delay-Doppler grid. FIG.3 shows an example of such a transmitter.

[0071] FIG.3 shows an example of generating an OTFS waveform. From left to right, source bits (e.g., data bits) are input to a number of FEC stages, each operating at a corresponding code rate. The FEC coded outputs are interleaved through corresponding interleavers. The resulting signals are mapped to symbols and mapped to a delay-Doppler grid along with pilot signals. The resulting mapped signal is processed through an OTFS modulator to generate n OTFS waveform.

[0072] 5. OTFS Modulator Examples

[0073] The OTFS modulator implements equation (1), generating a time-domain signal ^^^ ^^^. This equation may be implemented in multiple ways, such as using the Zak transform (see Section 3.1), a 2-dimensional transform such as a Fast Fourier Transform (FFT) that is a symplectic transform, or using Pulsones™. FIGS.4 to 6 show three examples for different implementations of equations (1) and (2), and FIG.7 gives an example for implementing equation (3). 165524628.2PCT Patent Application 119314.8090.WO00

[0074] FIG.4 shows a method of OTFS waveform generation in which the delta trains∆^^,^^^^^^^are multiplied by the delay-Doppler grid elements ^^^^^, ^^^. The resulting signal iscombined and convolved with ^^ఛ^^^^to obtain the output signal. Here, the signal is composed indomain.

[0075] FIG.5 shows an embodiment in which the convolution operation is performed before adding the resulting signals together. In other words, signal is composed in the Doppler domain.

[0076] FIG.6 shows the example where Pulsones™ are multiplied by grid elements and the result is combined to obtain the transmission waveform.

[0077] Note, that there may be other equivalent implementation of equations (1)-(3). For example, the time-domain signal can be rewritten as ெି^ ேି^^^^^^^^ൌ ^^ఛ^^^^∗ ^ ^^௧^^^^^ ^^^^^, ^^^∙ ^ ^^^ଶగ^∆ఔ^ఛ^^^൫ ^^ െ ^^Δ ^^ െ ^^ ^^^൯(4)

[0078]

[0079] 6.

[0080] In this section, we give further details on equalization in the delay-Doppler domain, when using OTFS with a set of predefined basis signals. For example, as described in the present document, the basis signals may combine certain mathematical properties of a pulse and a tone, and may be called Pulsones™.

[0081] Channel estimation may be performed by assigning to one or more delay-Doppler grid elements a known symbol (pilot) at the transmitter. At the receiver, the received signal may be processed for finding out the grid elements and their values where the pilot symbol was transformed to by the channel interaction.

[0082] Let’s consider a pilot symbol that was assigned at the transmitter to the grid location ൫ ^^^, ^^^൯, and received after the channel interaction at grid locations ^ ^^^, ^^^^ with received values ℎ^, for ^^ ൌ 1,2, … ,Ω.

[0083] To equalizeother than the pilot, a receiver will transform the estimated channel response obtained from the pilot to other locations on the grid, by rotating it: ℎ^^^^^, ^^^ൌ ℎ^ ∙ ^^^ଶగ∙^൫^,^,^^,^^,ே,ெ൯(5)

[0084] Herein, ^^^∙^is agrid dimensions ^^ ൈ ^^. That is, the receiver-side applies a rotation that isof the x- and y- coordinates of the grid location in the two-dimensional (2D) delay-Doppler grid, the x- 165524628.2PCT Patent Application 119314.8090.WO00 and y- coordinates of the pilot location in the 2D delay-Doppler grid, and the height and width dimensions of the 2D delay-Doppler grid.

[0085] In some embodiments, the equalization in the delay-Doppler domain that applies the rotation described above can be incorporated into the iterative decoder and iterative receiver architecture seen in FIGS.14 and 15 (which use a single FEC code), and FIGS.16 and 17 (which use an MLC FEC code), respectively.

[0086] The iterative decoder, illustrated in FIG.14, uses for an input the received delay-Dopplergrid of dimensions ^^ ൈ ^^. A received grid element is denoted by ^^^ ^^, ^^^, where ^^ ൌ 0,1, … , ^^ െ1 and ^^ ൌ 0,1, , … , ^^ െ 1. First, the channel estimation module, extracts the channel responseℎ, from the channel estimation area in the delay-Doppler grid. Then, a delay-Doppler equalizer generates A Posteriori probability estimation of the data symbols, ^^^^^^, based on ^^, ℎ and the a priori probability ^^^^ ^^^, which is fed-back from a previous iteration of the decoder. A symbol demapper module, computes bit Log-Likelihoods Ratios (LLRs), ^^, from the a posteriori probability, ^^^^^^. Extrinsic LLRs are derived by subtracting from ^^, the a priori LLRs, ^^^, computed in the previous iteration. The extrinsic LLRs may be deinterleaved and then they are fed into the FEC for decoding. If decoding is successful, the decoded information bits are passed to the next module following the iterative decoder for further processing. If decoding is not successful, the FEC will output coded bit LLRs, which may be interleaved and then fed into the symbol mapper as, ^^^. The symbol mapper computes symbol a priori symbol probabilities, ^^^^^^^, for the next iteration. Iterations are terminated, when there is a successful decoding in the FEC, or some other criterion is met, such as maximum number of iterations.

[0087] In general, iterative receivers exchange extrinsic information between the equalizer and the FEC decoder to achieve close to optimal performance, as shown in FIG.15 for an OTFS receiver 400. The extrinsic information may include a priori knowledge of which transmission resources (e.g., time slots of subcarriers) use which particular FEC. For example, the equalizer 402 uses prior information on the data symbols coming from the FEC feedback path to improve the equalization of the symbols. This feedback path comprises a symbol mapper 410 and OTFS transformation module 412. Then, these symbols are converted to bit likelihoods that are FEC decoded. Several iterations are performed until all the source data is decoded correctly, or until some other stopping criteria is met. An inverse OTFS transform module 404 may apply inverse OTFS transform and a symbol demapper 406 may recover bits from modulation symbols.

[0088] Compared to other techniques described next, the error-rate performance of the scheme 400 may be degraded. One reason for the degradation may be because of the mixture of bits 165524628.2PCT Patent Application 119314.8090.WO00 with different level of reliability in every FEC codeword that is being decoded. The constellation bits with low reliability make it harder for the FEC decoder to converge to the correct codeword and therefore, the feedback to the equalizer has less information to improve the equalization.

[0089] If the transmission processing was based on MLC, the basic iterative decoder is modified to accommodate it as well, e.g., using the iterative decoder in FIG.16. The LLRs from the symbol demapper are split into the different levels, optionally deinterleaved and then fed to the different FEC decoders. The coded bits LLRs output of the different FEC decoders are optionally interleaved and fed back to the symbol mapper.

[0090] When multi-level encoding is applied at the transmitter, the iterative receiver 550, in each decoding iteration, decodes only a part of the constellation bits. It typically starts with the most reliable bits and then proceeds in the next iterations to less reliable ones. This scheme, shown in FIG.17, allows the equalizer to receive in earlier iterations priors, which are dominant from the constellation symbols point of view and better improve the equalization. When the FEC has successfully decoded one level, it switches to decode the next one. The receiver continues to iterate until all levels have been decoded successfully or until some other stopping criteria is met. The most reliable bits are often bits that are used to decide the "macro" region within the constellation map where a symbol lies--e.g., the quadrant in which a constellation symbol of a 4 or 8 QAM signal lies, followed by sub-quadrant within the quadrant, and so on. Thus, as shown in FIG.17 the received signal may be equalized by the equalizer 402. In the forward path, the equalized signal may undergo an inverse OTFS transform (404), and the symbols from the resulting transformed signal may be demapped for decoding by multiple different FECs FEC1 to FECq (modules 558a to 558q). In the feedback path, the decoded symbol (bit) outputs of the FEC modules may be mapped to symbols (410) and transformed into OTFS domain signals (symbols) for feedback to the equalizer 402. As described above, in some implementations, different forward error correction codes are used for symbols from the multiple symbols corresponding to header and payload portions of the bits from the signal.

[0091] 7. Example OTFS Use Cases

[0092] An OTFS waveform generated as described herein may be described using Pulsones™ and may be used in a variety of different digital communication scenarios such as Under water acoustic wave communications, Deep-space communication, communication with non-terrestrial equipment such as satellites, airborne devices such as airplanes, balloons, drones, etc. The communication channel in such cases may comprise aerial-to-ground, ground-to-aerial or ariel- to-ariel communication, underwater acoustic wave communication deep space communication 165524628.2PCT Patent Application 119314.8090.WO00 and so on. Furthermore, the disclosed techniques may be applied in generally any frequency range - from sub-MHz (e.g., underwater acoustics that uses 10 Hz to 1 MHz), MHz, GHz or THz and beyond.

[0093] 8. OTFS Synchronization Examples

[0094] As disclosed herein, the mathematically infinite summation of a Pulsone™, may be truncated to the effective duration of the time window ^^௧. Therefore, multiple OTFS frames can be transmitted consecutively one after the other, as shown in FIG.11. As shown in FIG.11, multiple OTFS frames may be consecutively transmitted (or received) using multiple configurations. Here, each OTFS frame is characterized by a time window. The multiple frames may be: non-overlapping (top graph), or partially overlapping (bottom graph). The graphs show time dimension as horizontal axis and power or amplitude as the vertical axis.

[0095] To demodulate and decode the OTFS frames, a receiver should know where an OTFS frame begins. The duration of the frame is assumed to be known from a high-level configuration. One possible method for synchronization is to add a known transmitted signal at the beginning of every ^^, OTFS frames, where ^^ ^ 1, as shown in FIG.12. Multiple OTFS frames with synchronization sequences examples are shown in FIG.12. The multiple time windows and synchronization sequences may be: non-overlapping (top) or partially overlapping (bottom).

[0096] This known transmitted signal, which may also be referred to as a “Synchronization Sequence”, is a sequence of ^^^^symbols derived, for example from:

[0097] – A Zadoff-Chu sequence

[0098] – A pseudo-random sequence

[0099] – An m-sequence

[0100] – A Gold code sequence

[0101] Typically, these sequences are generated using a generation parameter, such as a seed or a root number.

[0102] The same Synchronization Sequence may be used each time, or at different instances of the sequence, a time-varying version of it may be used, according to rules known both to the transmitter and the receiver.

[0103] The length of the Synchronization Sequence, ^^^^, and its periodicity, ^^, are system parameters designed to meet different criterions such as SNR, latency, or throughput.

[0104] There may be situations, where an OTFS receiver may receive the signal of more than one OTFS transmitters. For example, a cellular network with multiple cells and a receiver at a cell edge, receiving the signal from more than one cell transmitters. In this case, the 165524628.2PCT Patent Application 119314.8090.WO00 Synchronization Sequence generation parameters (such as a seed, or a root) may be different for different transmitters.

[0105] Another implementation may use at the same transmitter, different Synchronization Sequences to convey information to the receiver. Each Synchronization Sequences then, corresponds to a different configuration of the system. The different Synchronization Sequences may be generated from different generation parameters. The receiver will detect which one of the Synchronization Sequence was transmitted and apply the associated configuration.

[0106] At the transmitter side, the Synchronization Sequence may be inserted before or afterapplying the delay pulse, ^^ఛ^^^^, as shown in FIGS. 13A and 13B.

[0107] Two implementation examples are depicted in FIGS.13A and 13B. FIG.13A shows a scheme for multiplexing Synchronization Sequence (SS) after a full OTFS signal is generated, and FIG.13B shows a scheme in which SS is multiplexed with the OTFS signal before the convolution with the delay pulse, ^^ఛ.

[0108] 9. Examples of Embodiments and Implementations

[0109] FIG.8 is a block diagram representation of a wireless hardware platform 800 which may be used to implement the various methods described in the present document. The hardware platform 800 may be incorporated within a base station or a user device. The hardware platform 800 includes a processor 802, a memory 804 (this may be optional and in some cases the memory may be internal to the processor) and a transceiver circuitry 806. The processor may execute instructions, e. g., by reading from the memory 804, and control the operation of the transceiver circuitry 806 and the hardware platform 800 to perform the methods described herein. In some embodiments, the memory 804 and / or the transceiver circuitry 806 may be partially or completely contained within the processor 802 (e.g., same semiconductor package).

[0110] The following solutions may be preferably implemented by some embodiments.

[0111] 1. A method of digital communication (e.g., method 900 depicted in FIG.9), comprising: receiving (902) a signal over a communication channel; determining (904) an estimate of the communication channel from one or more pilot symbols in the signal transmission, wherein the one or more pilot symbols are assigned along a delay-Doppler resource grid; equalizing (906) non-pilot symbols in the signal transmission by rotating the estimate of the communication channel according to grid locations of the one or more pilot symbols along the delay-Doppler resource grid at other grid locations; and recovering (908) data bits from the equalized non-pilot symbols. The method 900 may be implemented by a receiver (e.g., 102, 104 or 800). 165524628.2PCT Patent Application 119314.8090.WO00

[0112] 2. A method of digital communication (e.g., method 1000 depicted in FIG.10), comprising: generating (1002) a signal comprising one or more pilot symbols and one or more non-pilot symbols having transmission resources assigned along a delay-Doppler resource grid; and transmitting (1004) the signal over a communication channel; wherein the one or more pilot symbols are configured to enable a determination of an estimate of the transmission channel at a receiver; and wherein the one or more non-pilot symbols are configured to enable recovery of data bits from the one or more non-pilot symbols by rotating the estimate of the channel transmission based on grid locations of the one or more pilot symbols along the delay-Doppler resource grid at other grid locations. The method 900 may be implemented by a device that transmits signals (e.g., 102, 104 or 800).

[0113] 3. The method of solutions 1-2, wherein the one or more pilot symbols are mapped to grid locations ൫ ^^^, ^^^൯ at a transmitter-side and are received at grid locations^^^^, ^^^^at a receiver- values ℎ^, for ^^ ൌ 1,2, … ,Ω; and wherein the rotating the estimate at other grid determining:ℎ^^^ ^^, ^^^ ൌ ℎ^ ∙ ^^^ଶగ∙^൫^,^,^^,^^,ே,ெ൯where ^^^∙^is a location ൫ ^^ , ^^ ൯ and the grid^ ^dimensions ^^ ൈ ^^. In other words, in the two-dimensional (2D) delay- the receiver-side applies a rotation that is a function of the x- and y- coordinates of the grid location, the x- and y- coordinates of the pilot location, and the height and width dimensions of the grid.

[0114] 4. The method of any of solutions 1-3, wherein the signal is mathematically represented as a super-positions of a number of basis signals, represented in time domain as: ேି^ெି^^^^^^^ൌ ^ ^ ^^^^^^∙ ^^^^,^^^^^^where ^^^^^, ^^^are delay-signal is defined as ^ ^^^^,^^^^^^≜ ^^^∗ ^ ^^^∙ ^ ^^^ଶగ^∆ఔ^ఛ^^^ ^^ ^^where ^^ఛ^^^^operation, ^^௧^^^^ൌℱି^^ ^^ఔ^ is an inverse Fourier transform of a pulse in a Doppler domain, Δ ^^ ൌ ^^^ / ^^ and ∆ ^^ ൌఔ^ேare delay and Doppler grid resolutions, respectively, and ^^^∙^ is Dirac delta function. 5. The method of solution 4, where the signal is represented by an equivalent signal derived from a correct reordering the mathematical operations. For example, FIGS.4 to 6 and related description discloses different ways by which ordering may be performed. Different 165524628.2PCT Patent Application 119314.8090.WO00 mathematical interpretations of OTFS are also discussed in Sections 3.1-3.3. In some implementation, signal processing may be performed using analog or digital methods (e.g., numerical analysis) such that the final results approximately or exactly match results obtained from the above-described equations. Therefore, the sequence of steps is an example implementation, while other implementations may produce a result equivalent to the implementation steps explicitly discussed in the solutions.

[0116] 6. The method of any of solutions 1-5, wherein the signal is generated by: encoding the data bits using a forward error correction code, interleaving an output of the forward error correction, mapping an output of the interleaving to the one or more non-pilot symbols, and mapping the one or more non-pilot symbols to the delay-Doppler grid. Additional examples are disclosed in Sections 4, 5, and 6.

[0117] 7. The method of solution 6, wherein the signal is generated by performing an orthogonal time frequency space modulation that uses one of (1) a Zak transform, (2) a two- dimensional (2D) transform, or (3) the basis signals.

[0118] 8. The method of solution 7, wherein the 2D transform comprises a symplectic Fourier transform. In some cases, for finite dimensions, a symplectic transform may be mathematically characterized by a non-singular, skew-symmetric matrix multiplication.

[0119] 9. The method of any of solutions 1-8, wherein the communication channel comprises an underwater acoustic channel.

[0120] 10. The method of any of solutions 1-8, wherein the communication channel comprises an interstellar communication channel.

[0121] 11. The method of any of solutions 1-8, wherein the communication channel comprises an aerial-to-ground, a ground-to-aerial or an aerial-to-aerial communication channel.

[0122] 12. The method of any of solutions 1-11, wherein the signal is transmitted using wavelengths smaller than one millimeter. For example, the signal may be transmitted at a radio frequency in the fractional tera Hertz to multiples of tera Hertz range.

[0123] 13. The method of any of solutions 1-12, wherein the signal comprises multiple orthogonal time frequency space frames, each occupying a corresponding time window.

[0124] 14. The method of solution 13, wherein the time windows are overlapping with other neighboring time windows.

[0125] 15. The method of solution 14, wherein the time windows are non-overlapping.

[0126] 16. The method of solution 15, wherein at least some the time windows comprise intervening synchronization signals (SS). 165524628.2PCT Patent Application 119314.8090.WO00

[0127] 17. The method of solution 16, wherein SS are non-overlapping with neighboring time windows.

[0128] 18. The method of solution 16, wherein SS are partially overlapping with neighboring time windows.

[0129] 19. The method of any of solutions 16-18, wherein the SS are based on a synchronization sequence.

[0130] 20. The method of solution 19, wherein the synchronization sequence comprises a Zadoff-Chu sequence, a pseudo-random sequence, an m-sequence or a Gold code sequence.

[0131] 21. The method of any of solutions 19-20, wherein the synchronization sequence uniquely identifies a transmitter that generated the signal.

[0132] 22. The method of any of solutions 16-21, wherein the SS is inserted after applying a delay pulse during generation of the signal.

[0133] 23. The method of any of solutions 16-21, wherein the SS is inserted prior to applying a delay pulse during generation of the signal.

[0134] 24. The method of any of solutions 16-23, wherein the SS are designed to convey a configuration of a transmitter of the SS to a receiver of the SS.

[0135] 25. The method of solution 24, wherein the configuration comprises one or more of an orthogonal time frequency space parameter, a power parameter, a medium access control (MAC) layer parameter, a radio resource control (RRC) layer parameter or a physical (PHY) layer parameter.

[0136] When a receiver receives the signal that includes one or more SS, the receiver may identify the SS portion(s) of the signal. For example, the receiver may use blind decoding or autocorrelation based decoding for receiving the SS. Based on the SS portions, the receiver may obtain timing information for OTFS frames. Using the timing information, the receiver may decode the OTFS frame according to a technique disclosed herein. As a result of the decoding, the receiver may extract source bits that were transmitted over the signal that was received.

[0137] Furthermore, the receiver may use the received SS to determined configuration parameters of the transmitter, as described herein. In some embodiments, the SS itself may include a configuration parameter that provides a configuration of how SS are interspersed among OTFS frames.

[0138] Additional examples of solutions 13-25 are disclosed throughout the present document, including, e.g., section 8. 165524628.2PCT Patent Application 119314.8090.WO00

[0139] 26. An apparatus for digital communication comprising a processor and a transceiver, wherein the processor is configured to perform signal processing operations recited in any of solutions 1-25 and the transceiver is configured to transmit or receive the signal under control of the processor.

[0140] 27. A computer-readable medium having code stored thereon; the code, upon execution by a processor, causing the processor to implement a method recited in any of solutions 1-25.

[0141] It will be appreciated that the present document provides various techniques for generation, transmission and reception of OTFS signals, e.g., as described with reference to equations (1) and 2). It will further be appreciated that the present document discloses various modulator embodiments that perform OTFS modulation. In some disclosed embodiments, a receiver uses rotated versions of the channel estimation performed at pilot locations to obtain an estimate of the communication channel.

[0142] It will further be appreciated that the disclosed techniques are flexible and may be used in many different communication scenarios such as radio access networks (RANs) for mobile device communication in various frequency bands in the mega, giga or tera hertz ranges. In some embodiments, the disclosed techniques may be used in a fixed wireless access scenario in which a base station and / or user devices may be located at relatively stationary locations. Other application scenarios include use of the disclosed techniques using non-terrestrial equipment such as satellites, airborne devices such as airplanes, balloons, drones, etc. The communication channel in such cases may comprise aerial-to-ground, ground-to-aerial or ariel- to-ariel communication, underwater acoustic wave communication deep space communication and so on.

[0143] The disclosed and other embodiments, modules and the functional operations described in this document can be implemented in digital electronic circuitry, or in computer software, firmware, or hardware, including the structures disclosed in this document and their structural equivalents, or in combinations of one or more of them. The disclosed and other embodiments can be implemented as one or more computer program products, i.e., one or more modules of computer program instructions encoded on a computer readable medium for execution by, or to control the operation of, data processing apparatus. The computer readable medium can be a machine-readable storage device, a machine-readable storage substrate, a memory device, a composition of matter effecting a machine-readable propagated signal, or a combination of one or more them. The term “data processing apparatus” encompasses all apparatus, devices, and machines for processing data, including by way of example a programmable processor, a 165524628.2PCT Patent Application 119314.8090.WO00 computer, or multiple processors or computers. The apparatus can include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them. A propagated signal is an artificially generated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal, that is generated to encode information for transmission to suitable receiver apparatus.

[0144] A computer program (also known as a program, software, software application, script, or code) can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a standalone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program does not necessarily correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network.

[0145] The processes and logic flows described in this document can be performed by one or more programmable processors executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit).

[0146] Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read -only memory or a random access memory or both. The essential elements of a computer are a processor for performing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks. However, a computer need not have such devices. Computer readable media suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and 165524628.2PCT Patent Application 119314.8090.WO00 flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto optical disks; and CD ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.

[0147] While this patent document contains many specifics, these should not be construed as limitations on the scope of an invention that is claimed or of what may be claimed, but rather as descriptions of features specific to particular embodiments. Certain features that are described in this document in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable sub-combination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a sub-combination or a variation of a sub-combination. Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results.

[0148] Only a few examples and implementations are disclosed. Variations, modifications, and enhancements to the described examples and implementations and other implementations can be made based on what is disclosed. 165524628.2

Claims

PCT Patent Application 119314.8090.WO00 WHAT IS CLAIMED IS:

1. A method of digital communication, comprising: receiving a signal over a communication channel; determining an estimate of the communication channel from one or more pilot symbols in the signal, wherein the one or more pilot symbols are assigned along a delay-Doppler resource grid; equalizing one or more non-pilot symbols in the signal by rotating the estimate of the communication channel according to grid locations of the one or more pilot symbols along the delay-Doppler resource grid at other grid locations; and recovering data bits from one or more equalized non-pilot symbols.

2. A method of digital communication, comprising: generating a signal comprising one or more pilot symbols and one or more non-pilot symbols having transmission resources assigned along a delay-Doppler resource grid; and transmitting the signal over a communication channel, wherein the one or more pilot symbols are configured to enable (a) a determination of an estimate of the communication channel at a receiver, and (b) a recovery of data bits from the one or more non-pilot symbols by rotating the estimate of the communication channel based on grid locations of the one or more pilot symbols along the delay-Doppler resource grid at other grid locations.

3. The method of claim 1 or 2, wherein the one or more pilot symbols are mapped to grid locations ൫ ^^^, ^^^൯ at a transmitter-side and are received at grid locations ^ ^^^, ^^^^ at a receiver- side, values ℎ^, for ^^ ൌ 1,2, … ,Ω; and wherein theat other grid locations at the receiver-side comprisesℎ^^^ ^^, ^^^ ൌ ℎ^ ∙ ^^^ଶగ∙^൫^,^,^^,^^,ே,ெ൯where ^^^∙^ is alocation ൫ ^^^, ^^^൯ and grid dimensions ^^ ൈ ^^.

4. The method of claim 3, wherein the signal is mathematically represented as a super- positions of a number of basis signals, represented in time domain as: ேି^ெି^^^^165524628.2PCT Patent Application 119314.8090.WO00 where ^^^ ^^, ^^^ are delay-Doppler grid elements, and a basis signal is defined as ^ ^^^^,^^^^^^≜ ^^ఛ^^^^∗ ^ ^^௧^^^^∙ ^ ^^^ଶగ^∆ఔ^ఛ^^^൫ ^^ െ ^^Δ ^^ െ ^^ ^^^൯൩ where convolution operation, ^^௧^ ^^^ ൌ ℱି^^Δ ^^ ൌ ^^^ / ^^ and ∆ ^^ ൌఔ^ே are delay and Doppler grid resolutions, respectively, and ^^^∙^ is Dirac delta function.

5. The method of claim 1 or 2, wherein the signal is generated by: encoding the data bits using a forward error correction code, interleaving an output of the forward error correction code, mapping an output of the interleaving to the one or more non-pilot symbols, and mapping the one or more non-pilot symbols to the delay-Doppler resource grid.

6. The method of claim 5, wherein the signal is generated by performing an orthogonal time frequency space modulation that uses one of (1) a Zak transform, (2) a two-dimensional (2D) transform, or (3) one or more basis signals.

7. The method of claim 6, wherein the 2D transform comprises a symplectic Fourier transform.

8. The method of claim 1 or 2, wherein the communication channel comprises an underwater acoustic channel.

9. The method of claim 1 or 2, wherein the communication channel comprises an interstellar communication channel.

10. The method of claim 1 or 2, wherein the communication channel comprises an aerial-to- ground, a ground-to-aerial or an aerial-to-aerial communication channel.

11. The method of claim 1 or 2, wherein the signal is transmitted using wavelengths smaller than one millimeter.

12. The method of claim 1 or 2, wherein the signal comprises multiple orthogonal time frequency space frames, each occupying a corresponding time window. 165524628.2PCT Patent Application 119314.8090.WO00 13. The method of claim 12, wherein time windows are overlapping with other neighboring time windows.

14. The method of claim 12, wherein time windows are non-overlapping.

15. The method of claim 14, wherein at least some of the time windows comprise intervening synchronization signals (SS).

16. The method of claim 15, wherein SS are non-overlapping with neighboring time windows.

17. The method of claim 15, wherein SS are partially overlapping with neighboring time windows.

18. The method of claim 15, wherein the SS are based on a synchronization sequence.

19. The method of claim 18, wherein the synchronization sequence comprises a Zadoff-Chu sequence, a pseudo-random sequence, an m-sequence, or a Gold code sequence.

20. The method of claim 18, wherein the synchronization sequence uniquely identifies a transmitter that generated the signal.

21. The method of claim 15, wherein the SS are inserted after applying a delay pulse during generation of the signal.

22. The method of claim 15, wherein the SS are inserted prior to applying a delay pulse during generation of the signal.

23. The method of claim 15, wherein the SS are designed to convey a configuration of a transmitter of the SS to a receiver of the SS.

24. The method of claim 23, wherein the configuration comprises one or more of an orthogonal time frequency space (OTFS) parameter, a power parameter, a medium access control (MAC) layer parameter, a radio resource control (RRC) parameter, or a physical (PHY) layer parameter.

26. An apparatus for digital communication comprising a processor and a transceiver, wherein the processor is configured to perform signal processing operations recited in any of 165524628.2PCT Patent Application 119314.8090.WO00 claims 1 to 24 and the transceiver is configured to transmit or receive the signal under control of the processor.

27. A computer-readable medium having code stored thereon; the code, upon execution by a processor, causing the processor to implement the method recited in any of claims 1 to 24. 165524628.2

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