Orthogonal time-frequency-space signal communication using predefined base signals

Abstract

Methods and systems are described for orthogonal time-frequency-space (OTFS) communication using a predefined base signal. 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. One or more pilot symbols are allocated along a latency-Doppler resource grid herein. The method further includes equalizing non-pilot symbols in the signal transmission by rotating an estimate of the communication channel at other grid positions according to grid positions of one or more pilot symbols along the delay-Doppler resource grid, and recovering data bits from the equalized non-pilot symbols.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This patent document claims priority to U.S. Provisional Patent Application No. 63 / 487,725, filed on March 1, 2023, the entire disclosure of which is hereby incorporated by reference. Technical Field

[0003] This document relates to digital communications, and more particularly, to data modulation schemes for digital communications in wireless systems. Background Art

[0004] Due to the dramatic growth in the number of wireless user devices and the amount of wireless data these devices can generate or consume, current wireless communication networks are rapidly running out of bandwidth to accommodate this high growth in data traffic and to provide high quality of service to users.

[0005] Various efforts are underway in the telecommunications industry to come up with next generation wireless technologies that can meet the performance demands of wireless devices and networks.Many of these activities involve situations where a large number of user devices can be served by a network. Summary of the Invention

[0006] This document discloses techniques that can be used by wireless networks to achieve several operational improvements. Specifically, a method for generating a waveform known as Orthogonal-Time-Frequency-Space (OTFS) is disclosed. For example, an OTFS waveform may use a waveform known as Pulsones. TM is generated using a predefined base signal.

[0007] In one example aspect, a digital communication method is disclosed. The method includes receiving a signal via a communication channel; and determining an estimate of the communication channel based on one or more pilot symbols in the signal. In this example, the one or more pilot symbols are allocated 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 at other grid positions based on the grid positions of the one or more pilot symbols along the delay-Doppler resource grid, and recovering data bits from the one or more equalized non-pilot symbols.

[0008] In another example aspect, another method of digital communication is disclosed. The method includes generating a signal including one or more pilot symbols and one or more non-pilot symbols, the one or more pilot symbols and the one or more non-pilot symbols having transmission resources allocated along a time-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) determining, at a receiver, an estimate of the communication channel, and (b) recovering data bits from the one or more non-pilot symbols by rotating the estimate of the communication channel at other grid locations based on grid locations of the one or more pilot symbols along the time-delay-Doppler resource grid.

[0009] In another example aspect, a wireless communication apparatus implementing the methods described above is disclosed. The wireless communication apparatus can include a transmitter circuit and / or a receiver circuit to perform signal transmission or reception, and a processor to implement various signal processing techniques described in this document.

[0010] In yet another example aspect, a wireless system in which one or more of the above-described methods are implemented is disclosed.

[0011] In yet another example aspect, the method can be embodied as processor-executable code, and can be stored on a computer-readable program medium.

[0012] These and other features are described in this document. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 An example communication network is shown.

[0014] Figure 2 A simplified example of a wireless communication system in which uplink and downlink transmissions are performed is shown.

[0015] Figure 3 A block diagram of an example of a transmitter is shown.

[0016] Figure 4 A block diagram of an embodiment of signal generation is shown.

[0017] Figure 5 A block diagram of another embodiment of signal generation is shown.

[0018] Figure 6 A block diagram of yet another embodiment of signal generation is shown.

[0019] Figure 7 A block diagram of an example implementation is shown.

[0020] Figure 8 An example of a hardware platform is shown.

[0021] Figure 9 andFigure 10 is a flowchart of various example methods for digital communications.

[0022] Figure 11 Examples of fully and partially overlapping OTFS frames are shown.

[0023] Figure 12 Examples of multiple OTFS frames with intervening synchronization signals (SS) are shown.

[0024] Figure 13A and Figure 13B Implementation examples of generating OTFS waveforms including synchronization signals are shown.

[0025] Figure 14 Examples of iterative decoders in which a single forward error correction (FEC) code is processed are depicted.

[0026] Figure 15 A block diagram of an example iterative receiver apparatus is shown.

[0027] Figure 16 Examples of iterative decoder architectures when using multi-level coded (MLC) FEC codes are shown.

[0028] Figure 17 A block diagram of an example iterative receiver apparatus using multi-level decoding is shown. DETAILED DESCRIPTION

[0029] For the purposes of this disclosure, the technical solutions and advantages will be more apparent from the following detailed description with reference to the drawings. Unless otherwise stated, embodiments and features in the embodiments of this document can be combined with each other.

[0030] The use of section headings in this document is for ease of reading only and does not limit or otherwise constrain the discussion or embodiments to the section headings only. Further, certain standard-specific terminology is used for illustrative purposes only and the disclosed technology is applicable to any wireless communication system.

[0031] 1. Example of a wireless communication environment

[0032] The wireless or time-varying nature of the communication channel presents several challenges in designing a transmission protocol suitable for a wireless communication scenario. Today, users expect their wireless devices to work everywhere and in various moving or stationary situations.

[0033] Relative motion of the transmitter and receiver with respect to each other causes signal distortion, such as varying channel delay, Doppler and / or angular spread, signal degradation due to ground and sea clutter, and the like. Another example of signal degradation is flat fading, where the entire channel occupied by a transmission will experience fading or attenuation, which can be relatively constant across the entire channel. In practice, it can be desirable to design a transmission scheme to fit within a particular link budget, maximum power constraint, or linearity of the electronics used to send or receive the signal.

[0034] 2. Example Wireless System

[0035] Figure 1 An example of a wireless communication system 100 is shown in which a transmitter device 102 sends a signal to a receiver 104. As depicted, the signal can experience various wireless channels and multipath. Some reflectors, such as buildings and trees, can be static, while other reflectors, such as cars, can be mobile scatterers. The transmitter device 102 can be, for example, a user device, a mobile phone, a tablet, a computer, or another Internet of Things (IoT) device such as a smart watch, and a camera, among others. The receiver device 104 can be a network device such as a base station. Signals sent from the base station to the transmitter 102 can experience similar channel degradation produced by static or mobile scatterers. The techniques described in this document can be implemented by devices in the wireless communication system 100. The terms “transmitter” and “receiver” are used for ease of explanation only. As described further herein, depending on the direction of transmission (uplink or downlink), a network station can either transmit or receive, and a user device can either receive or transmit.

[0036] Figure 2 A simplified wireless network is shown to highlight certain aspects of the disclosed technology. In a wireless network, a transmitter sends wireless signals to a receiver. For some transmissions in the network, variously referred to as downlink transmissions 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 receivers of those wireless signals. For some other transmissions, the direction of transmission can be reversed, as depicted in FIG. 1. Figure 2 Such transmissions are often referred to as uplink transmissions or upstream transmissions. For such transmissions, one or more user devices act as transmitters of wireless signals, and a network-side node such as a base station acts as a receiver of those signals (as depicted in FIG. 1). Figure 2Other types of transmissions in the network can include device-to-device transmissions, sometimes referred to as direct or sidelink transmissions. While the term "downlink" and "uplink" are used primarily for convenience in this document, similar techniques can also be used for other cases in which transmissions in both directions are performed, e.g., inbound or incoming transmissions received by a wireless device and outbound or outcoming transmissions sent by a wireless device. For example, a downlink transmission can be an inbound transmission to a user device but an outbound transmission to a network device. Similarly, an uplink transmission can be an inbound transmission to a network device but an outbound transmission from a wireless device. Thus, for some embodiments, the disclosed techniques can also be described using terms such as "inbound" and "outbound" transmissions without introducing any 3GPP-specific or other wireless protocol-specific meaning into the terms "uplink" and "downlink."

[0037] In a frequency-division multiplexing (FDM) network, transmissions to and from a base station can occupy different frequency bands (each of which can occupy contiguous or non-contiguous spectrum). In a time-division multiplexing (TDM) network, transmissions to and from a base station occupy the same frequency band but are separated in the time domain using a TDM mechanism such as time-slot-based transmissions.

[0038] 3. OTFS Waveform Overview

[0039] OTFS waveforms are constructed from symbols allocated to a grid in a two-dimensional domain called time-delay-Doppler. The grid is characterized by a Doppler period v p , typically satisfying v p ≥ 2 · f d , where f d is the maximum expected Doppler shift and a time-delay period τ p = 1 / v p . The grid has N cells along Doppler and N cells along time-delay, where BW is the bandwidth of the OTFS signal and T is its duration. In addition to information-carrying symbols (typically quadrature amplitude modulation, QAM), the grid can include pilot symbols for channel detection and estimation.

[0040] An OTFS waveform in the time domain can be thought of as a superposition of Pulsones TM multiplied by the grid cells

[0041]

[0042] where x[n, m] is a time-delay-Doppler grid cell, and Pulsones TM are defined as

[0043]

[0044] where, ρ τ (t) is the impulse in the time-delay domain, the symbol * denotes the convolution operation, is the inverse Fourier transform of the impulse in the Doppler domain, Δτ = τ p / M and Δν = v p / N are the time-delay resolution and the Doppler grid resolution, respectively, and δ(·) is the Dirac delta function. Typically, Pulsones TM can be considered as a basis signal for the time-delay-Doppler grid.

[0045] In this document, we will use the notation to denote the second term of equation (2), which represents an infinite δ sequence with a rotated phase multiplied by a time window:

[0046]

[0047] In practical implementations, the infinite sum of equation (3) can be truncated to the effective duration of the time window W t .

[0048] 3.1 Example implementation using Zak theory

[0049] In signal processing, signals (or waveforms) are traditionally represented in the time or frequency domain. Each representation reveals different properties of the signal. The dictionary between these two representations is the Fourier transform:

[0050] (0.1)

[0051] Interestingly, there exists another domain in which signals can be naturally represented. This domain is called the time-delay-Doppler domain. For the purpose of this discussion, this is also called the Zak domain. In its simplest form, a Zak signal is a function of two variables The variable τ is called the time-delay and the variable v is called the Doppler. Assume that the function is periodic along τ with period v r and quasi-periodic along τ with period τ r . The quasi-periodic condition is given by:

[0052] (0.2)

[0053] For each one Assume that the periods satisfy the Nyquist condition τr ·v r = 1. The Zak domain signal is transformed by a canonical transformation called the time and frequency Zak transform. and is related to the time and frequency domain signals. More precisely, if Representing the Hilbert space of the Zak signal, the time and frequency Zak transform is a linear transformation:

[0054] (0.3)

[0055] (0.4)

[0056] and The Fourier transform of This factorization is sometimes called the Zak factorization. The Zak decomposition embodies the combinatorial mathematics of the Fast Fourier Transform algorithm. In other words, the Zak transform is essentially a geometric projection: the time Zak transform is an integral along the Doppler variable, and dually, the frequency Zak transform is an integral along the delay variable.

[0057] We now proceed to provide an overview of OTFS modulation. The key point to note is that the Zak transform plays the same role for OTFS as the Fourier transform does for OFDM. More specifically, in OTFS, the information bits are encoded as Zak signals x(τ, v) in the delay-Doppler domain and transmitted using the following rules:

[0058] (0.5)

[0059] Among them, w* σ x(τ, v) represents a two-dimensional filtering operation using a two-dimensional pulse w(τ, ν) using an operation *σ called warped convolution (which will be explained in this document). The conversion to the physical time domain is done using the Zak transform. Equation (0.5) should be contrasted with similar formulas in the case of frequency division multiple access FDMA and time division multiple access TDMA. In FDMA, the information bits are encoded in the frequency domain as a signal x(f) and transmitted according to the following rule:

[0060] (0.6)FDMA(x)=FT(w(f)*x(f)),

[0061] where filtering is performed in the frequency domain by linear convolution with a one-dimensional pulse w(f) (in the case of standard OFDM w(f) is equal to the sinc function). The modulation mapping is the Fourier transform. In TDMA, the information bits are encoded in the time domain as a signal x(t) and sent according to the following rules:

[0062] (0.7) TDMA(x) = Id(w(t) * x(t)),

[0063] where filtering is done in the time domain by a linear convolution with the one-dimensional pulse w(t). In this case, the modulation map is the identity map.

[0064] 3.2 Example implementations based on realization theory

[0065] In some embodiments, the OTFS transceiver can be mathematically explained from the point of view of realization theory. In short, in the present approach, the signal space of the waveform is seen as a representation space of a Heisenberg group, or equivalently as a Hilbert space equipped with a set of Heisenberg operators each associated with a different point in the time delay Doppler plane. This representation space allows for a variety of realizations. Two standard realizations are the time realization and the frequency realization, and they are linked by a one-dimensional Fourier transform. In communication theory, the TDMA transceiver structure naturally fits the time realization since the QAM symbols are multiplexed along the time coordinate, while the OFDM transceiver structure naturally fits the frequency realization since the QAM symbols are multiplexed along the frequency coordinate. The main observation is that there exists a canonical realization between the time realization and the frequency realization, called the Zak realization. Interestingly, the waveforms in the Zak realization are represented as functions on the two-dimensional time delay Doppler domain satisfying certain quasi-periodic conditions. The main message of the present description is that the Zak realization naturally fits the OTFS transceiver. Observing the OTFS transceiver from this perspective extends its novelty and independence from other existing transceiver structures.

[0066] 3.3 Example implementation using the time delay-Doppler grid

[0067] A time delay-Doppler grid is an integer span of a pair of linearly independent vectors g1, g2 e V. In more detail, given such a pair, the associated grid is the set:

[0068]

[0069] The vectors g1and g2are called lattice basis vectors. It is convenient to arrange the basis vectors as the first and second columns of a matrix G, i.e.,

[0070] (2.2)

[0071] is called the basis matrix. In this way, the grid is the image of the standard grid under the matrix G. The volume of the grid is by definition the area of the fundamental domain, which equals the absolute value of the determinant of G. Each one of the grids allows for a symplectic reciprocal grid, also called the orthogonal complementary grid, which we denote by ⊥ ⊥ The definition of ​

[0072] (2.3)

[0073] If we call Λ under-sampled. If Λ = Λ ⊥ we call Λ critically-sampled. Alternatively, the volume of the fundamental domain of an under-sampled grid is ≥ 1. From this point on, we only consider under-sampled grids. Given a grid Λ, we define its maximal rectangular sub-grid as where:

[0074] (2.4) τ r = arg min {τ > 0 : (τ, 0) e Λ}

[0075] (2.5) v = arg min {v > 0 : (0, v) e Λ},

[0076] When τ r or v r are infinite, we define Λ r = {0}. If Λ = Λ r we say that the grid Λ is rectangular. Obviously, the sub-grids of a rectangular grid are also rectangular. A rectangular grid is under-sampled if τ r v r ≥ 1. A standard example of a critically-sampled rectangular grid is generated by the identity matrix:

[0077] (2.6)

[0078] An important example of a non-rectangular critically-sampled grid is the hexagonal grid Λ hex generated by the basis matrix:

[0079] (2.7)

[0080] where An interesting property of the hexagonal grid is that it has the longest distance between adjacent points among all critically-sampled grids. The maximal rectangular sub-grid Λ hex is generated by g1and 2g2-g1.

[0081] In some embodiments, the OTFS transceiver structure depends on the choice of the following parameters: a critically-sampled grid a filter function and an information grid specified by We assume that the filter function is factored as w(τ, v) = w τ (τ) w v (v), where the delay and Doppler factors are about Δτ = τ rN and Av = v r / M square root Nyquist. We encode the information bits as a periodic two-dimensional sequence of QAM symbols x = x[nAT, mAv] with period (N, M). Multiplying x by the standard Zak signal P, we obtain the Zak signal xP. Considering xP in particular as the unique quasi-periodic extension of the finite sequence x[nAT, mAv] with n = 0,.., N - 1 and m = 0,.., M - 1. We define the modulated transmit waveform as:

[0082] (3.1)

[0083]

[0084] As described in the example above, OTFS modulation proceeds in three steps. In the first step, the information block x is quasi-periodized, thus converted into a discrete Zak signal. In the second step, the bandwidth and time duration of the signal are shaped by a two-dimensional filtering process defined by a twist convolution with the pulse w. In the third step, the filtered signal is transformed to the time domain by applying the Zak transform. To better understand the structure of the transmit waveform, we apply a few simple algebraic manipulations to (3.1). First, we note that, as an interlacing operator, the Zak transform obeys the following relation:

[0085] (3.2)

[0086] Second, we note that the factorization w(τ, v) = w τ (τ)w v (v) can be expressed as a twist convolution w = w τ * σw v . Thus, we can write:

[0087] (3.3)

[0088]

[0089] where W t = FT -1 (w v ) and * denotes linear convolution in time. We refer to the waveform as the raw OTFS waveform. As can be seen from (3.3), the transmit waveform is obtained from the raw waveform by windowing in time followed by a convolution with the pulse. This cascading operation is the time representation of the two-dimensional filtering in the Zak domain. It is beneficial to study the structure of the raw OTFS waveform in the case where it supports x at a single grid point, i.e., composed of a single QAM symbol (i.e., x = δ(nAT, mAv)). In this case, it can be shown that the raw waveform takes the following form:

[0090] (3.4)

[0091] In other words, the original waveform is the pulse rate An infinite delta pulse sequence of shift and phase modulation, where the shift is determined by the time delay parameter n and the modulation is determined by the Doppler parameter m. For demodulation mapping, given the received waveform In the case of

[0092] (3.5)

[0093] where w ★ Depend on Given a matched filter, we usually incorporate an additional step of sampling yat(nΔτ, mΔv) for n=0, .., N-1, and m=0, .., M-1.

[0094] 4. OTFS transmitter example

[0095] 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 L), interleaves the encoded bits and maps them into symbols (typically QAM), and then assigns the symbols to delay-Doppler grid cells. Some of the delay-Doppler grid cells may not be assigned any symbols (zero values), while other grid cells may be assigned known symbols (pilots). Finally, the OTFS modulator is applied to the delay-Doppler grid. Figure 3 An example of such a transmitter is shown.

[0096] Figure 3 An example of generating an OTFS waveform is shown. From left to right, source bits (e.g., data bits) are input to multiple FEC stages, each operating at a corresponding code rate. The FEC-encoded output is interleaved by a corresponding interleaver. The resulting signal is mapped to symbols and, along with a pilot signal, mapped to a delay-Doppler grid. The resulting mapped signal is processed by an OTFS modulator to generate n OTFS waveforms.

[0097] 5. OTFS modulator example

[0098] The OTFS modulator implements equation (1) which generates the time domain signal s(t). This equation can be implemented in a variety of ways, such as using the Zak transform (see Section 3.1), a two-dimensional transform such as the Fast Fourier Transform (FFT) which is a symplectic transform, or using Pulsones TM . Figure 4 to Figure 6Three examples are shown for different implementations of equations (1) and (2), and Figure 7 An example is given for implementing equation (3).

[0099] Figure 4 An OTFS waveform generation method is shown, where a delta sequence is multiplied by the delay-Doppler grid cells x[n,m]. The resulting signals are combined and convolved with p τ (t) to obtain the output signal. Here, the signal is composed in the delay domain.

[0100] Figure 5 An embodiment is shown where the convolution operation is performed before the resulting signals are added together. In other words, the signal is composed in the Doppler domain.

[0101] Figure 6 An instance is shown where Pulsones TM are multiplied by the grid cells and the results are combined to obtain the transmit waveform.

[0102] Note that there can be other equivalent implementations of equations (1)-(3). For example, the time-domain signal can be rewritten as:

[0103]

[0104] which can be implemented in a different architecture than the given examples.

[0105] 6. OTFS receiver example

[0106] In this section, we give further details about equalization in the delay-Doppler domain when using OTFS with a set of predetermined basis signals. For example, as described in this document, the basis signals can combine certain mathematical properties of pulses and tones, and can be referred to as Pulsones TM .

[0107] Channel estimation can be performed by assigning known symbols (pilots) to one or more delay-Doppler grid cells at the transmitter. At the receiver, the received signal can be processed to find out which grid cells the pilot symbols have been transformed to by the channel interaction, and the values of these grid cells.

[0108] Let us consider a pilot symbol that is assigned to a grid location (n p ,m p ) at the transmitter, and is received at a grid location (n i ,m i ) after the channel interaction and has a received value h i for i = 1, 2, …, Ω.

[0109] To equalize the symbols other than the pilot, the receiver will transform the estimated channel response obtained from the pilot by rotating it to other locations on the grid:

[0110]

[0111] Here, f(·) is a function of the grid location (n, m), the pilot location (n p ,m p ), and the grid dimensions N x M. That is, the rotation applied at the receiver side is a function of the x and y coordinates of the grid location in the 2D delay-Doppler grid, the x 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.

[0112] In some embodiments, the equalization in the delay-Doppler domain, which applies the rotation described above, can be incorporated into the iterative decoder and iterative receiver architecture structures shown in Figure 14 and Figure 15 (which use a single FEC code) and Figure 16 and Figure 17 (which use MLC FEC codes), respectively.

[0113] Figure 14 The iterative decoder illustrated in FIG. 1 uses a received delay-Doppler grid of dimensions N x M as input. The received grid elements are denoted by y[n, m], where n = 0, 1,..., N - 1 and m = 0, 1,..., M - 1. First, a channel estimation module extracts the channel response h from the channel estimation region in delay-Doppler. Then, a delay-Doppler equalizer generates the a posteriori probability estimate p(x) of the data symbols based on y, h, and the a priori probabilities p a (x) (which are fed back from the previous iteration of the decoder). A symbol de-mapper module computes the bit log-likelihood ratios (LLRs) λ from the a posteriori probabilities p(x). The extrinsic LLRs are derived by subtracting the a priori LLRs λ a computed in the previous iteration from λ. The extrinsic LLRs can be de-interleaved and then fed into the FEC for decoding. If the decoding is successful, the decoded information bits are passed to the next module after the iterative decoder for further processing. If the decoding is not successful, the FEC outputs the coded bit LLRs, which can be interleaved and then fed into the symbol mapper as λ a . The symbol mapper computes the a priori symbol probabilities p a (x) of the symbols for the next iteration. The iteration is terminated when there is a successful decoding in the FEC, or some other criteria such as a maximum number of iterations is met.

[0114] Generally, iterative receivers exchange extrinsic information between the equalizer and the FEC decoder to achieve near-optimal performance, as in Figure 15 shown in FIG. 4 for an OTFS receiver 400. The extrinsic information can include a priori knowledge about which transmission resources (e.g., time slots of subcarriers) use which particular FEC. For example, the equalizer 402 uses prior information about the data symbols from the FEC feedback path to improve the equalization of the symbols. This feedback path includes a symbol mapper 410 and an OTFS transform module 412. These symbols are then converted to bit likelihood values that are decoded by the FEC. Several iterations are performed until all of the source data is correctly decoded, or until some other stopping criterion is met. An inverse OTFS transform module 404 can apply an inverse OTFS transform, and a symbol demapper 406 can recover the bits from the modulated symbols.

[0115] The error rate performance of the scheme 400 can degrade compared to other techniques described next. One reason for the degradation can be due to the mixing of bits with different reliability levels in each FEC codeword being decoded. Constellation bits with low reliability make it more difficult for the FEC decoder to converge to the correct codeword, and thus, the feedback to the equalizer has less information to improve the equalization.

[0116] If the transmission processing is based on MLC, then the basic iterative decoder is also modified to accommodate it, e.g., using the iterative decoder in Figure 16 The LLRs from the symbol demapper are split into different levels, optionally deinterleaved, and then fed to different FEC decoders. The encoded bit LLR outputs of the different FEC decoders are optionally interleaved and fed back to the symbol mapper.

[0117] When multi-level encoding is applied at the transmitter, the iterative receiver 550 decodes only a portion of the constellation bits in each decoding iteration. It generally starts with the most reliable bits and then proceeds to less reliable bits in the next iteration. Figure 17 This scheme, shown in FIG. 5, allows the equalizer to receive a priori information in earlier iterations that is dominant from a constellation symbol perspective and better improves the equalization. When the FEC has successfully decoded one level, it switches to decoding the next level. The receiver continues iterating until all levels have been successfully decoded or until some other stopping criterion is met. The most reliable bits are generally the ones that are used to decide the “macro” region within which a symbol lies - e.g., the quadrant that a constellation symbol of a 4QAM signal or an 8QAM signal lies in, followed by sub-quadrants within the quadrant, and so on. Thus, as in Figure 17As shown in the middle, the received signal can be equalized by equalizer 402. In the forward path, the equalized signal can undergo an inverse OTFS transform (404), and the symbols from the resulting transformed signal can be de-mapped for decoding by a plurality of different FECs FEC1 to FECq (modules 558a to 558q). In the feedback path, the decoded symbol (bit) outputs of the FEC modules can be mapped to symbols (410) and converted to OTFS domain signals (symbols) for feedback to equalizer 402. As described above, in some implementations, different forward error correction codes are used for symbols from a plurality of symbols corresponding to header and payload portions of bits from the signal.

[0118] 7. Example OTFS use cases

[0119] As described herein, the generated OTFS waveforms can use Pulsones TM to describe and can be used for various different digital communication scenarios, such as underwater acoustic communication, deep space communication, communication with non-terrestrial devices (such as satellites), airborne devices (such as airplanes, balloons, drones), etc. In this case, the communication channel can include air-to-ground, ground-to-air, or air-to-air communication, underwater acoustic communication, and deep space communication, etc. Moreover, the disclosed technology can generally be applied to any frequency range - from below MHz (e.g., using underwater acoustics of 10 Hz to 1 MHz), MHz, GHz, or THz and above.

[0120] 8. OTFS synchronization examples

[0121] As disclosed herein, the mathematical infinite summation of a Pulsone TM can be truncated to an effective duration of a time window W t . Thus, as shown in Figure 11 , a plurality of OTFS frames can be transmitted consecutively one after another. As shown in Figure 11 , a plurality of OTFS frames can be transmitted (or received) consecutively using a plurality of configurations. Here, each OTFS frame is characterized by a time window. The plurality of frames can be: non-overlapping (top figure), or partially overlapping (bottom figure). These figures show the time dimension as the horizontal axis and the power or amplitude as the vertical axis.

[0122] To demodulate and decode an OTFS frame, the receiver should know the location where the OTFS frame starts. The duration of the frame is assumed to be known from higher layer configuration. As shown in Figure 12 , one possible method for synchronization is to add a known transmitted signal at the start of every S OTFS frames, where S > 1. Figure 12A number of OTFS frames with synchronization sequence examples are shown in Figure 1. The number of time windows and synchronization sequences can be non-overlapping (top figure) or partially overlapping (bottom figure).

[0123] The known transmitted signal (which can also be referred to as a "synchronization sequence") is a sequence of N ss symbols, for example, derived from:

[0124] - Zadoff-Chu sequences

[0125] - pseudo-random sequences

[0126] - m-sequences

[0127] - Gold code sequences

[0128] Typically, these sequences are generated using a generation parameter, such as a seed or a root number.

[0129] The same synchronization sequence can be used each time, or in different instances of the sequence, a time-varying version of the sequence can be used according to rules known to the transmitter and receiver.

[0130] The length N ss of the synchronization sequence and its period S are system parameters designed to meet different criteria, such as SNR, latency or throughput.

[0131] There can be cases in which an OTFS receiver can receive the signal of more than one OTFS transmitter. For example, a cellular network with multiple cells and a receiver at the edge of a cell receiving signals from more than one cell transmitter. In this case, the synchronization sequence generation parameters, such as seeds or roots, can be different for different transmitters.

[0132] Another implementation can use different synchronization sequences at the same transmitter to convey information to the receiver. Each synchronization sequence then corresponds to a different configuration of the system. The different synchronization sequences can be generated from different generation parameters. The receiver will detect which of the synchronization sequences was transmitted and apply the associated configuration.

[0133] At the transmitter side, as shown in Figure 13A and Figure 13B , the synchronization sequence can be inserted before or after the application of the delay impulse p τ (t).

[0134] Two implementation examples are depicted in Figure 13A and Figure 13B . Figure 13A A scheme for multiplexing the synchronization sequence (SS) after the generation of the complete OTFS signal is shown, and Figure 13BFigure 1 shows a diagram of an OTFS signal and a time delay pulse p τ A scheme for multiplexing the SS with the OTFS signal before convolution.

[0135] 9. Examples of embodiments and implementations

[0136] Figure 8 is a block diagram representation of a wireless hardware platform 800 that can be used to implement the various methods described in this document. The hardware platform 800 can be incorporated within a base station or a user equipment. The hardware platform 800 comprises a processor 802, a memory 804 (which can be optional and in some cases the memory can be internal to the processor) and a transceiver circuit 806. The processor can execute instructions, for example by reading from the memory 804, and control the operation of the transceiver circuit 806 and the hardware platform 800 to perform the methods described herein. In some embodiments, the memory 804 and / or the transceiver circuit 806 can be partially or completely contained within the processor 802 (e.g. the same semiconductor package).

[0137] The following solutions can preferably be implemented by some embodiments.

[0138] 1. A method of digital communication (e.g. Figure 9 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 allocated along a time-delay-doppler resource grid; equalizing (906) non-pilot symbols in the signal transmission by rotating the estimate of the communication channel at other grid locations according to grid locations of the one or more pilot symbols along the time-delay-doppler resource grid; and recovering (908) data bits from the equalized non-pilot symbols. The method 900 can be implemented by a receiver (e.g. 102, 104 or 800).

[0139] 2. A method of digital communication (e.g. Figure 10 Method 1000 depicted in FIG. 10), comprising generating (1002) a signal comprising one or more pilot symbols and one or more non-pilot symbols, the one or more pilot symbols and the one or more non-pilot symbols having transmission resources allocated along a time-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 a recovery of data bits from the one or more non-pilot symbols by rotating the estimate of the channel transmission at other grid locations based on grid locations of the one or more pilot symbols along the time-delay-doppler resource grid. The method 900 can be implemented by a device transmitting the signal (e.g. 102, 104 or 800).

[0140] 3. The method of solutions 1-2, wherein one or more pilot symbols are mapped at the transmitter side to grid positions (n p ,m p ) and received at the receiver side at grid positions (n i ,m i ) with received values h i for i = 1, 2,..., Q; and wherein rotating the estimate at other grid positions comprises determining

[0141]

[0142] where f(·) is a function of the grid position (n, m), the pilot position (n p ,m p ) and the grid dimensions N x M. In other words, in a two-dimensional (2D) delay-Doppler grid, the receiver side applies a rotation that is a function of the x and y coordinates of the grid position, the x and y coordinates of the pilot position and the height and width dimensions of the grid.

[0143] 4. The method of any of solutions 1-3, wherein the signal is mathematically represented as a superposition of a plurality of basis signals, represented in the time domain as:

[0144]

[0145] where x[n, m] is a delay-Doppler grid cell, and the basis signals are defined as:

[0146]

[0147] where p τ (t) is an impulse in the delay domain, the symbol * denotes a convolution operation, is the inverse Fourier transform of an impulse in the Doppler domain, AT = T p / M and are the delay resolution and Doppler grid resolution, respectively, and d(·) is the Dirac delta function.

[0148] 5. The method of solution 4, wherein the signal is represented by an equivalent signal derived from the mathematical operation with correct reordering. For example, Figure 4 to Figure 6Different ways in which ordering can be performed are disclosed in the related description. Different mathematical interpretations of OTFS are also discussed in Sections 3.1-3.3. In some implementations, signal processing can be performed using analog or digital methods (e.g., numerical analysis) such that the final results approximately or exactly match the results obtained from the equations described above. Thus, the sequence of steps is an example implementation, and other implementations can produce results that are equivalent to the implementation steps discussed explicitly in the solution.

[0149] 6. The method of any of solutions 1-5, wherein the signal is generated by encoding data bits using a forward error correction code, interleaving the output of the forward error correction, mapping the interleaved output to one or more non-pilot symbols, and mapping the one or more non-pilot symbols to a delay-Doppler grid. Further examples are disclosed in Sections 4, 5, and 6.

[0150] 7. The method of solution 6, wherein the signal is generated by performing a quadrature time-frequency-space modulation using one of (1) a Zak transform, (2) a two-dimensional (2D) transform, or (3) a basis signal.

[0151] 8. The method of solution 7, wherein the 2D transform comprises a symplectic Fourier transform. In some cases, for finite dimensions, the symplectic transform can be mathematically characterized by a non-singular skew-symmetric matrix multiplication.

[0152] 9. The method of any of solutions 1-8, wherein the communication channel comprises an underwater acoustic wave channel.

[0153] 10. The method of any of solutions 1-8, wherein the communication channel comprises an interstellar communication channel.

[0154] 11. The method of any of solutions 1-8, wherein the communication channel comprises an air-to-ground, ground-to-air, or air-to-air communication channel.

[0155] 12. The method of any of solutions 1-11, wherein the signal is transmitted using a wavelength less than 1 millimeter. For example, the signal can be transmitted at a radio frequency in a range of fractions of terahertz to multiples of terahertz.

[0156] 13. The method of any of solutions 1-12, wherein the signal comprises a plurality of quadrature time-frequency-space frames, each quadrature time-frequency-space frame occupying a respective time window.

[0157] 14. The method of solution 13, wherein the time window overlaps with other adjacent time windows.

[0158] 15. The method of solution 14, wherein the time windows are non-overlapping.

[0159] 16. The method of solution 15, wherein at least some of the time windows comprise an intervening synchronization signal (SS).

[0160] 17. The method of solution 16, wherein the SS does not overlap with an adjacent time window.

[0161] 18. The method of solution 16, wherein the SS partially overlaps with an adjacent time window.

[0162] 19. The method of any of solutions 16-18, wherein the SS is based on a synchronization sequence.

[0163] 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.

[0164] 21. The method of any of solutions 19-20, wherein the synchronization sequence uniquely identifies a transmitter that generated the signal.

[0165] 22. The method of any of solutions 16-21, wherein the SS is inserted after applying the time delay pulse during generation of the signal.

[0166] 23. The method of any of solutions 16-21, wherein the SS is inserted before applying the time delay pulse during generation of the signal.

[0167] 24. The method of any of solutions 16-23, wherein the SS is designed to convey a configuration of a transmitter of the SS to a receiver of the SS.

[0168] 25. The method of solution 24, wherein the configuration contains one or more of a quadrature 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.

[0169] When a receiver receives a signal comprising one or more SSs, the receiver can identify the SS portion of the signal. For example, the receiver can receive the SS using blind decoding or autocorrelation-based decoding. Based on the SS portion, the receiver can obtain timing information of the OTFS frame. Using the timing information, the receiver can decode the OTFS frame according to the techniques disclosed herein. As a result of the decoding, the receiver can extract source bits transmitted on the received signal.

[0170] Further, as described herein, a receiver can use the received SS to determine configuration parameters of the transmitter. In some embodiments, the SS itself can include configuration parameters that provide a configuration of how the SS is spread out in the OTFS frame.

[0171] Further examples of solutions 13-25 are disclosed throughout this document, including, e.g., Section 8.

[0172] 26. An apparatus for digital communications, comprising a processor and a transceiver, wherein the processor is configured to perform the signal processing operations recited in any of solutions 1-25, and the transceiver is configured to transmit or receive signals under the control of the processor.

[0173] 27. A computer readable medium having code stored thereon; the code, when executed by a processor, causes the processor to implement the method recited in any of solutions 1-25.

[0174] It will be appreciated that this document provides various techniques for generating, transmitting, and receiving OTFS signals, e.g., as described with reference to equations (1) and (2). It will also be appreciated that this document discloses various modulator embodiments that perform OTFS modulation. In some disclosed embodiments, a receiver uses a rotated version of channel estimation performed at pilot locations to obtain an estimate of the communication channel.

[0175] It will be further appreciated that the disclosed techniques are flexible and can be used in many different communication scenarios, such as a radio access network (RAN) for mobile device communications in various frequency bands in the megahertz, gigahertz, or terahertz range. In some embodiments, the disclosed techniques can be used in fixed wireless access scenarios, where base stations and / or user devices can be located in relatively static locations. Other application scenarios include the use of the disclosed techniques using non-terrestrial devices such as satellites, airborne devices such as airplanes, balloons, drones, etc. In such cases, the communication channel can include air-to-ground, ground-to-air, or air-to-air communications, underwater acoustic wave communications, and deep space communications, etc.

[0176] 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 of them. The term "data processing apparatus" encompasses all apparatus, devices, and machines for processing data, including by way of example a programmable processor, a 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. The 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.

[0177] 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 stand-alone 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 are interconnected by a communication network.

[0178] 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 special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit) and apparatuses can also be implemented as special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit).

[0179] 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 executing 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 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.

[0180] Although this patent document contains many details, these should not be construed as limiting the scope of the invention or of what can be claimed, but as merely describing a particular implementation of features. Certain features that are described in this document in the context of separate embodiments can also be implemented in combination with each other. Conversely, various features that are described in the context of a single embodiment can also be implemented separately from each other. Moreover, although features can 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 can be directed to a subcombination or variation of a subcombination. Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring this particular order, or the order in which the operations are illustrated, and the order of the operations can be changed, or two or more operations can be performed at the same time, or operations can be performed with additional operations not depicted.

[0181] Only a few examples and implementations are disclosed. Many variations, modifications, and enhancements of the described examples and implementations and other implementations can be made based on what is disclosed.

Claims

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 allocated along a time-delay-Doppler resource grid; equalizing one or more non-pilot symbols in the signal by rotating the estimate of the communication channel at other grid locations according to grid locations of the one or more pilot symbols along the time-delay-Doppler resource grid; and recovering data bits from the 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, the one or more pilot symbols and the one or more non-pilot symbols having transmission resources allocated along a time-delay-Doppler resource grid; and transmitting the signal over a communication channel, wherein the one or more pilot symbols are configured to enable (a) determining an estimate of the communication channel at a receiver, and (b) recovering data bits from the one or more non-pilot symbols by rotating the estimate of the communication channel at other grid locations based on grid locations of the one or more pilot symbols along the time-delay-Doppler resource grid. the signal is mathematically represented as a superposition of a plurality of basis signals, represented in time domain as:

3. The method of claim 1 or 2, wherein, The one or more pilot symbols are mapped at the transmitter side to grid positions (n p ,m p ) and received at the receiver side at grid positions (n i ,m i ) for i = 1, 2,..., Ω with received values h i ; and wherein rotating the estimate at the receiver side at other grid positions comprises determining: where f(·) is a function of the grid location (n, m), the pilot location (n p ,m p ), and the grid dimensions N x M.

4. The method of claim 3, wherein, where x[n,m] is a time-delay-Doppler grid cell, and a basis signal is defined as: the signal is generated by: where p(t) is the transmitted pulse, and τ (t) is the time-delayed pulse, and the symbol * denotes convolution, is the inverse Fourier transform of the pulse in Doppler domain, and p / M and are the time-delay resolution and the Doppler grid resolution, respectively, and is the Dirac delta function.

5. The method of claim 1 or 2, wherein, encoding the data bits using a forward error correction code, interleaving an output of the forward error correction code, mapping the interleaved output to the one or more non-pilot symbols, and mapping the one or more non-pilot symbols to the time-delay-Doppler resource grid. the signal is generated by performing orthogonal time frequency space modulation using one of (1) a Zak transform, (2) a two-dimensional (2D) transform, or (3) one or more basis signals.

6. The method of claim 5, wherein, the 2D transform comprises a symplectic Fourier transform.

7. The method of claim 6, wherein, the communication channel comprises an underwater acoustic channel.

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

9. The method of claim 1 or 2, wherein, the communication channel comprises an air-to-ground, ground-to-air, or air-to-air communication channel.

10. The method of claim 1 or 2, wherein, the signal is transmitted using a wavelength less than 1 millimeter.

11. The method of claim 1 or 2, wherein, the signal comprises a plurality of orthogonal time frequency space frames, each orthogonal time frequency space frame occupying a respective time window.

12. The method of claim 1 or 2, wherein, a time window overlaps with other adjacent time windows.

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

14. The method of claim 12, wherein, at least some of the time windows comprise an intervening synchronization signal (SS).

15. The method according to claim 14, wherein the SS does not overlap with adjacent time windows.

16. The method of claim 15, wherein, the SS partially overlaps with adjacent time windows.

17. The method according to claim 15, wherein: the SS is based on a synchronization sequence.

18. The method of claim 15, wherein, the synchronization sequence comprises a Zadoff-Chu sequence, a pseudo-random sequence, an m-sequence, or a Gold code sequence.

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

20. The method of claim 18, wherein, the SS is inserted after applying a time delay pulse during generation of the signal.

21. The method of claim 15, wherein, the SS is inserted before applying a time delay pulse during generation of the signal.

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

23. The method of claim 15, wherein, ​ 24. The method of claim 23, wherein, The configuration includes one or more of orthogonal time frequency space (OTFS) parameters, power parameters, medium access control (MAC) layer parameters, radio resource control (RRC) parameters, or physical (PHY) layer parameters.

25. An apparatus for digital communication, the apparatus comprising a processor and a transceiver, wherein, The processor is configured to perform the signal processing operations recited in any of claims 1-24, and the transceiver is configured to transmit or receive the signal under control of the processor.

26. A computer readable medium having stored thereon code, which, when executed by a processor, causes the processor to implement the method recited in any of claims 1-24.

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