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WO2025166301A1 - Traitement de signal pilote dans le domaine retard-doppler - Google Patents

Traitement de signal pilote dans le domaine retard-doppler

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Publication number
WO2025166301A1
WO2025166301A1 PCT/US2025/014206 US2025014206W WO2025166301A1 WO 2025166301 A1 WO2025166301 A1 WO 2025166301A1 US 2025014206 W US2025014206 W US 2025014206W WO 2025166301 A1 WO2025166301 A1 WO 2025166301A1
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WO
WIPO (PCT)
Prior art keywords
delay
doppler
signal
pulse
otfs
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Pending
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PCT/US2025/014206
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English (en)
Inventor
Shlomo Selim Rakib
Yoav Hebron
Ronny Hadani
Shachar Kons
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Cohere Technologies Inc
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Cohere Technologies Inc
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Publication of WO2025166301A1 publication Critical patent/WO2025166301A1/fr
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Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2626—Arrangements specific to the transmitter only
    • H04L27/2627—Modulators
    • H04L27/2639—Modulators using other transforms, e.g. discrete cosine transforms, Orthogonal Time Frequency and Space [OTFS] or hermetic transforms
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/69—Spread spectrum techniques
    • H04B1/7163—Spread spectrum techniques using impulse radio
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L5/00—Arrangements affording multiple use of the transmission path

Definitions

  • BACKGROUND [003] 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. [004] 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 [005] This document discloses techniques that may be used by communication networks to achieve several operational improvements. [006] In one example aspect, a method of transmitting a signal is disclosed.
  • the method includes generating a two-dimensional delay-Doppler signal comprising a sum of an information signal and a reference signal, wherein the sum is performed in delay-Doppler domain; and generating a transmission waveform from the two-dimensional delay-Doppler signal.
  • the method includes generating a transmission waveform as a summation of a first signal component and a second signal component, wherein the sum is performed in a time domain; wherein the first signal component comprises a reference signal, wherein the second signal component is generated by transforming a two-dimensional information signal from a delay-Doppler domain to a time domain, 170688394.5 Attorney Docket No.: 119314.8121.WO00 [008] In yet another aspect, a method of receiving a signal is disclosed.
  • the method includes receiving a received signal over a transmission channel, determining, by processing the received signal in a delay-Doppler domain, an estimate of cross-correlation between the received signal and a known reference signal that makes up the received signal, and estimating a delay-Doppler domain channel characteristic of the transmission channel based on the estimate of cross-correlation.
  • another method of transmitting a signal includes generating a transmission waveform as a summation of a first signal component and a second signal component, wherein the first signal component comprises an information signal modulated with a standard pulse-tone, and wherein the second signal component comprises a rotated pulse-tone.
  • FIG.1 shows an example communication network.
  • FIG.2 shows a simplified example of a wireless communication system in which uplink and downlink transmissions are performed.
  • FIG.3 shows an example OTFS modulation block diagram with a transmitter and a receiver.
  • FIG.4 shows an example flowchart for OTFS processing.
  • FIG.5 shows an example arrangement of reference signal (RS) antenna ports multiplexed in the delay-Doppler domain.
  • RS reference signal
  • FIG.6 shows an example pictorial depiction of the relationship between time, frequency, and ZAK domains.
  • FIG.7 shows an example pictorial depiction of the periodic and quasi-periodic nature of an information grid in the Zak domain.
  • FIG.8 shows an example of a graphical representation of an OTFS waveform.
  • FIG.9 shows an example block diagram of an OTFS communication system.
  • FIG.10 illustrates components of an example OTFS transceiver.
  • FIG.11 shows a block diagram of an example iterative receiver apparatus.
  • FIG.12 shows a block diagram of an example iterative receiver apparatus that uses multi-level decoding.
  • FIG.13 shows a block diagram of an example 2-D iterative equalizer.
  • FIG.14 depicts an example of an iterative decoder in which a single forward error correction (FEC) code is processed.
  • FIG.15 shows an example of an iterative decoder architecture for multi-level-coding (MLC) FEC.
  • FIG.16 is an illustration of an example channel equation.
  • FIG.17 shows an example of an iterative decoder architecture for improved channel estimation, through the decoder’s iterations.
  • FIG.18 depicts a two-antenna multi-input multi-output (MIMO) example.
  • MIMO multi-input multi-output
  • FIG.19 shows a pictorial depiction of a pulse-tone waveform.
  • FIG.20 depicts a visual example of a pulse-tone as a delay-Doppler domain waveform.
  • FIG.21 shows a pictorial representation of a pulse-tone being invariant under the Heisenberg Uncertainty Principle (HUP).
  • HUP Heisenberg Uncertainty Principle
  • FIG.22 is a pictorial depiction of a quasi-periodic pulse.
  • FIG.23 is a pictorial depiction of a quasi-periodic pulse – work around HUP.
  • FIG.24 depicts an example operation of a Zak transform implementation.
  • FIG.25 depicts an example of communication with pulse-tones.
  • FIG.26 shows a depiction of a crystalline regime along the delay-Doppler domain.
  • FIG.27 illustrates three fundamental signal representations.
  • FIG.28 shows examples of channel coupling in the TDM/FDM regimes.
  • FIG.29 shows examples of channel coupling in a crystalline regime.
  • FIG.30 shows a visual representation of aliasing versus the crystallization condition.
  • FIG.31 shows visual representations of aliasing in the FDM and TDM regimes.
  • FIG.32 shows a visual representation of a crystalline regime.
  • FIG.33 shows an example of radar sensing in a crystalline regime.
  • FIG.34 depicts an example of a joint communication and sensing system with a pair of unbiased pulse-tones.
  • FIG.35 shows an example of a transmitter-side method of reference signal overlaying an information signal.
  • FIG.36 shows an example of a transmitter-side method of reference signal overlaying an information signal.
  • FIG.37 shows an example of distortions caused by a channel.
  • FIG.38 shows an example of a hardware platform.
  • FIGS.39A–39D are flowcharts for example methods of facilitating digital communication.
  • 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.
  • 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.
  • 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.
  • the direction of transmission may be reversed.
  • Such transmissions are often called uplink or upstream 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.
  • downlink transmissions may be inbound transmissions for a user device, while outbound transmissions for a network device.
  • uplink transmission may be inbound transmissions for a network device while outbound transmissions from a wireless device.
  • 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.”
  • FDM frequency division multiplexing
  • TDM time division multiplexing
  • 5G solutions are expected to include massive MIMO antenna arrays of up to 256 antenna elements. These require a large number of reference signals to be multiplexed in order 170688394.5 Attorney Docket No.: 119314.8121.WO00 to simultaneously estimate the channels to and from the UEs.
  • the reference signal overhead is a crucial component in determining the overall throughput of the link.
  • Reference signals are typically placed in the time-frequency domain to assist the receiver in estimating the channel, generally in a coarse (regular or irregular) grid, as in LTE. Multiple antenna ports are multiplexed on the same coarse grid using different (ideally orthogonal) signature sequences. However, this orthogonality is often lost after transmission through the channel.
  • the present document provides, among other aspects, improvements to the OTFS technology by disclosing methods for inserting pilot or reference signals in the transmitted waveforms and correspondingly receiving signals that include pilot or reference signals, and process and use the pilot or reference signals for channel estimation. [0066] 4.1.
  • Orthogonal Time Frequency Space (OTFS) modulation is a modulation scheme whereby each transmitted symbol experiences a near-constant channel gain even in channels with high Doppler, large antenna arrays (massive MIMO), or at high frequencies such as millimeter waves.
  • OTFS modulates each information symbol onto one of a set of two- dimensional (2D) orthogonal basis functions that span the bandwidth and time duration of the transmission burst or packet.
  • the modulation basis function set of OTFS is specifically derived to combat the dynamics of the time-varying multipath channel.
  • OTFS can be implemented as a 170688394.5 Attorney Docket No.: 119314.8121.WO00 pre- and post-processing block to filtered OFDM systems, thus enabling architectural compatibility with LTE.
  • the main premise behind OTFS is to transform the time-varying multipath channel into a two-dimensional channel in the delay-Doppler domain. Through this transformation, all symbols over a transmission frame experience the same channel gain. That is because OTFS extracts the full diversity of the channel across time and frequency. This full diversity property of OTFS greatly reduces system overhead and the complexity associated with physical layer adaptation. It also presents the application layer with a robust fixed-rate channel, which is highly desirable in many of the delay-sensitive applications envisioned for 5G.
  • OTFS full diversity enables linear scaling of throughput with the number of antennas, regardless of channel Doppler.
  • OTFS enables dense and flexible packing of reference signals, a key requirement to support the large antenna arrays used in massive MIMO applications.
  • OTFS is designed so that its information symbols experience minimal cross-interference as well as full diversity in the delay-Doppler domain through appropriate design of the modulation lattice and pulse shape design in that domain.
  • OTFS as a modulation matches wireless channel characteristics through two processing steps; a transmitter first maps the two-dimensional delay-Doppler domain, where the information symbols (e.g., QAM symbols) reside (e.g., placed on a lattice or grid in the 2-D delay-Doppler domain), to the time-frequency domain through a combination of the inverse symplectic Fourier transform and windowing (e.g., each QAM symbol is spread throughout the time-frequency plane/domain). It then applies the Heisenberg transform to the time-frequency modulated signal to convert it into the time domain for transmission. A receiver performs the reverse operations.
  • the information symbols e.g., QAM symbols
  • windowing e.g., each QAM symbol is spread throughout the time-frequency plane/domain
  • OTFS works in the delay-Doppler coordinate system using a set of basis functions orthogonal to both time and frequency shifts. Both data and reference signals or pilots are carried in this coordinate system.
  • the delay-Doppler domain mirrors the geometry of the wireless channel, which changes far more slowly than the phase changes experienced in the 170688394.5 Attorney Docket No.: 119314.8121.WO00 rapidly varying time-frequency domain.
  • OTFS symbols experience the full diversity of the channel over time and frequency, trading latency for performance in high Doppler scenarios.
  • the complex baseband channel impulse response h( ⁇ ,v) characterizes the channel response to an impulse with delay ⁇ and Doppler v.
  • the received signal due to an input signal s(t) transmitted over this channel is given by .
  • (1) can also be interpreted as a linear operator ⁇ h( ⁇ ), parameterized by the impulse response h( ⁇ ,v), that operates on the input s(t) to produce the output r(t): .
  • OTFS modulation In the mathematics ⁇ h parameterized by a function h( ⁇ ,v) and operating on a function s(t) as defined in (2) is called a Heisenberg transform.
  • OTFS modulation also utilizes a Heisenberg transform on the transmitted symbols, hence the received signal becomes a cascade of two Heisenberg transforms, one corresponding to the OTFS modulation, and the other corresponding to the channel.
  • the corresponding structure of the received signal results in a near-constant gain on each of the transmitted symbols as well as a particularly simple mechanism to recover these symbols.
  • 4.1.2 OTFS Modulation [0077] OTFS modulation is comprised of a cascade of two two-dimensional transforms at both the transmitter and the receiver, as shown in FIG 3.
  • the transmitter first maps the information symbols x[n,m] residing (e.g., along the points of the reciprocal lattice ⁇ ⁇ ) in the two- Doppler domain to symbols X[n,m] (e.g., residing along the points of the lattice ⁇ ) in the time-frequency domain through a combination of the inverse symplectic Fourier transform and windowing. This cascade of operations is called the OTFS transform. Next the Heisenberg transform is applied to X[n,m] to convert the time-frequency modulated signal to the 170688394.5 Attorney Docket No.: 119314.8121.WO00 time domain signal s(t) for transmission over the channel.
  • Time-Frequency Modulation is a generic description of time-frequency modulation, which has the following components: A lattice or grid ⁇ in the time-frequency domain that is a sampling of the time and frequency axes at intervals T and ⁇ f respectively: .
  • a time-frequency modulator with these components maps the two-dimensional symbols X[n,m] on the lattice ⁇ to a transmitted waveform s(t) via a superposition of delay-and- operations on the pulse waveform gtx(t), namely (5)
  • Modulation of the OFDM transform mapping modulated symbols in the domain i.e., on each subcarrier to the transmitted signal in the time domain.
  • the received symbol X[n,m] is the same as the transmitted symbol except for a complex scale factor H[n,m], similar to OFDM transmitted through time-invariant frequency-selective fading
  • H[n,m] similar to OFDM transmitted through time-invariant frequency-selective fading
  • OTFS transforms utilize a variant of the standard Fourier transform called the Symplectic Finite Fourier Transform (SFFT). This transform is defined as follows. Let X p [n,m] denote the periodized version of X[n,m] with period (N,M).
  • SFFT Symplectic Finite Fourier Transform
  • OTFS can be defined as a time-frequency modulation with an additional pre-processing step.
  • OTFS incorporates a transmit windowing square summable function W tx [n,m] that multiplies the modulation symbols in the time-frequency domain.
  • W tx [n,m] the modulated symbols in OTFS can be defined as follows: . (21) [00101]
  • the transmitted defined in (6). (21) is called the OTFS transform, which combines an inverse symplectic transform with a windowing operation.
  • the second equation describes the Heisenberg transform of gtx(t) parameterized by the symbols X[n,m] into the transmitted signal s(t).
  • composition 170688394.5 Attorney Docket No.: 119314.8121.WO00 of these two transforms can comprise OTFS modulation, as depicted in the two transmitter blocks of FIG.3.
  • a different basis function representation useful in the OTFS demodulation process, discussed below, is as follows: [00103] The basis function b k , l [n,m] in the time-frequency domain. [00104] OTFS Demodulation: Let the receiver employ a receive windowing square summable function Wrx[n,m]. Then the demodulation operation can include the following steps: [00105] 1) Take the Wigner transform of the received signal, which yields .
  • 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.
  • FEC forward error correction
  • QAM symbol constellation levels
  • 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).
  • the OTFS modulator is applied to the delay-Doppler grid.
  • source bits e.g., data bits
  • 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 an OTFS waveform.
  • the OTFS waveform in the time domain may be considered to be a super-position of waveforms that are a combination of a pulse and a tone, called a pulse-tone, (one example being a PulsoneTM) multiplied by the grid elements ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ , ⁇ [00118] where ⁇ ⁇ ⁇ , ⁇ ⁇ are of a pulse-tone waveform) is defined as ⁇ ⁇ ⁇ , ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ [00119] where operation, ⁇ a ⁇ ⁇ ⁇ / ⁇ and ⁇ ⁇ ⁇ / ⁇ are the delay and Doppler grid resolutions, respectively, and ⁇ is the Dirac delta function.
  • the pulse-tones may be considered to be basis signals used for the delay-Doppler grid.
  • ⁇ ⁇ , ⁇ ⁇ ⁇ for the second term of (33), which represents an infinite delta train, with rotating by a time window: 170688394.5
  • the OTFS This equation may be implemented in multiple ways, such as using the Zak transform, a 2- dimensional transform, or using pulse-tones
  • a method of OTFS waveform generation in which the delta trains ⁇ ⁇ , ⁇ ⁇ ⁇ are multiplied by the delay-Doppler grid elements ⁇ , ⁇ is provided in an exemplary embodiment.
  • the resulting signal is combined and convolved with ⁇ ⁇ ⁇ ⁇ ⁇ to obtain the output signal.
  • the signal is composed in the delay domain.
  • the convolution operation is performed before adding the resulting signals together.
  • signal is composed in the Doppler domain.
  • pulse-tones are multiplied by grid elements and the result is combined to obtain the transmission waveform.
  • the time-domain signal can be rewritten as ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ , ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ [00126] [00127] 4.1.2.6 OTFS Receiver [00128]
  • the OTFS transform can include pre- and post-processing blocks to the OFDM modulator and demodulator in the transmitter and receiver respectively, as depicted in FIG 4. It should be noted that the OTFS modulation can also be derived as a pre- and post-processing of multicarrier systems other than OFDM (e.g., filter bank multicarrier).
  • OTFS Receiver Examples [00130]
  • the basis signals may combine certain mathematical properties of a pulse and a tone, and may be called a pulse-tone or a Pulsone.
  • Channel estimation may be performed by assigning to one or more delay-Doppler grid elements a known symbol (pilot) at the transmitter.
  • 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.
  • OTFS Multiplexing There are a variety of ways to multiplex several uplink or downlink transmissions in one OTFS frame. The most natural one is multiplexing in the delay-Doppler domain, such that different sets of OTFS basis functions, or sets of information symbols or resource blocks can be given to different users. Given the orthogonality of the basis functions, the users can be separated at the receiver. For the downlink, the UE (user equipment) need only demodulate the portion of the OTFS frame that is assigned to it.
  • the OTFS signals from all users extend over the whole time-frequency window, thus providing full diversity; that is, for a channel with Q clustered reflectors (Q multipath components separable in either the delay or Doppler dimension) the OTFS modulation can achieve a diversity order equal to Q. Furthermore, this full spreading is also advantageous from a Peak to Average Power Ratio (PAPR) point of view.
  • PAPR Peak to Average Power Ratio
  • PAPR peak-to-average power ratio
  • Low PAPR is an important goal for modulation/multiple access design since it reduces the maximum linear power requirements for the transmit amplifiers. This is particularly important for the uplink of cellular systems, since amplifiers in consumer devices such as handsets need to be low-cost.
  • OTFS (considered here with delay/Doppler multiplexing) can reduce uplink PAPR in two ways: (i) if a user is assigned a single Doppler frequency, then the PAPR is the same as for single-carrier transmission, i.e., significantly lower than for OFDM.
  • the packet transmission can extend over a longer 170688394.5 Attorney Docket No.: 119314.8121.WO00 period of time than in OFDM which allows to increase the maximum energy per bit under Tx power constraints. This is particularly relevant for short packets.
  • OTFS can achieve a superior trade-off between PAPR and performance compared to SC-FDMA, even in time-invariant channels. While SC-FDMA can have low PAPR during the active signal duration, the overall PAPR is only small if the signal has a duty cycle close to unity, which in turn requires that (due to the small packet size) it utilizes only a single (or very few) subcarriers.
  • OTFS can obtain full spreading in time and frequency while keeping the PAPR low.
  • OTFS reference signals or pilots are carried in the delay-Doppler domain as impulses to probe the channel. Each pilot has a space reserved around it to account for the maximum delay and Doppler spread of the channel. Like the information symbols, the pilots experience the same time and frequency diversity of the channel over the full observation bandwidth and time.
  • FIG.5 shows an example of such an arrangement of RS antenna ports (e.g., as RS impulses) in the delay-Doppler domain. Notice that each antenna port RS in FIG.5 is generally affected by a different channel.
  • the multiplexed reference signals are sampled in the time-frequency domain according to a selected coarse grid that does not overlap with the data grid points. This enables the observation window for estimating the channel from the reference signals to be independent of the data. Importantly, it also allows OTFS reference signals to be utilized for both OTFS as well as any multicarrier modulation, including OFDM and other proposed 5G waveforms. [00143] Because the reference signals are multiplexed in the delay-Doppler plane, which mirrors the geometry of the wireless channel, they can be very densely packed, based on the delay and Doppler characteristics of the channels.
  • further efficiency can be 170688394.5 Attorney Docket No.: 119314.8121.WO00 obtained with knowledge of channel conditions for different users or groups of users by flexibly assigning the users or groups different pilot spacing in the delay-Doppler domain. [00144] 5. Zak transforms [00145] Wireless devices may attempt to join a network while the channel between the wireless device and a base station may be impaired both in delay and in Doppler domains due to the movement of the wireless device and multi-path echoes between the wireless device and the base station. In a similar manner, the theoretical framework for operation of radars in detecting objects that could be moving, also benefits from waveforms that show similar robustness properties as the random access waveforms in the wireless domain.
  • signal transmissions in a wireless network may be represented by describing the waveforms in the time domain, in the frequency domain, or in the delay-Doppler domain (e.g., Zak domain). Because these three represent three different ways of describing the signals, signal in one domain can be converted into signal in the other domain via a transform.
  • a time-Zak transform may be used to convert from Zak domain to time domain.
  • a frequency-Zak transform may be used to convert from the Zak domain to the frequency domain.
  • the Fourier transform (or its inverse) may be used to convert between the time and frequency domains.
  • a Zak signal is a function ⁇ ⁇ ⁇ , ⁇ ⁇ of two variables.
  • the variable ⁇ is called delay and the variable ⁇ is called ⁇ ⁇ ⁇ , ⁇ ⁇ is assumed to be periodic along ⁇ with period ⁇ r and quasi-periodic along ⁇ ⁇ r .
  • Zak domain signals are related to time and frequency domain signals through canonical transforms ⁇ t and ⁇ f called the time and frequency Zak transforms.
  • the time and frequency Zak transforms are linear transformations: ⁇ t : ⁇ z ⁇ L 2 ⁇ t ⁇ ⁇ , (36) ⁇ f : ⁇ z ⁇ L 2 ⁇ f ⁇ ⁇ , (37) 170688394.5 Attorney Docket No.: 119314.8121.WO00 [00149]
  • Zak factorization This factorization is sometimes referred to as the Zak factorization.
  • the Zak embodies the combinatorics of the fast Fourier transform algorithm.
  • the precise for the Zak transforms will be given in the sequel. At this point it is enough to say that they 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.
  • the different signal domains and the transformations connecting between them are depicted in FIG.6.
  • FIG.6 The different signal domains and the transformations connecting between them are depicted in FIG.6.
  • the information bits are encoded on the delay-Doppler domain as a Zak signal x ⁇ ⁇ , ⁇ ⁇ and transmitted through the rule: OTFS ⁇ x ⁇ t ⁇ w ⁇ x ⁇ ⁇ , ⁇ ⁇ ⁇ , (38) [00151] where w ⁇ ⁇ x ⁇ ⁇ , ⁇ ⁇ w ⁇ ⁇ , ⁇ ⁇ ⁇ ⁇ called twisted convolution (to be explained in the present . The conversion to the physical time domain is done using the Zak transform. [00152] 5.1 Zak Theory [00153] In this section we describe the Zak realization of the signal space. A Zak realization depends on a choice of a parameter.
  • a delay-Doppler lattice is an integral span of a pair of linear independent vectors g 1, g 2 ⁇ V .
  • the associated lattice is the set: ⁇ ⁇ ⁇ a1 g 1 ⁇ a 2 g 2 : a 1 , a 2 ⁇ ⁇ , (39) 170688394.5 Attorney Docket No.: 119314.8121.WO00 [00156]
  • the vectors g 1 and g 2 are called the lattice basis vectors. It is convenient to arrange the basis vectors as the first and second columns of a matrix G , i.e.,: ⁇
  • the volume of the definition the area of the fundamental domain which is equal to the absolute value of of G. Every lattice admits a symplectic reciprocal lattice, aka orthogonal complement lattice that we denote by ⁇ ⁇ .
  • the definition of ⁇ ⁇ is: ⁇ ⁇ v ⁇ V : ⁇ ⁇ v , ⁇ ⁇ ⁇ for every ⁇ ⁇ ⁇ , (41) [00158]
  • ⁇ is . say that ⁇ is critically sampled if ⁇ ⁇ ⁇ ⁇ .
  • an under-sampled lattice is such that the volume of its fundamental domain is > 1. From this point on we consider only under-sampled lattices.
  • the standard example of a critically sampled rectangular lattice is ⁇ rec ⁇ ⁇ ⁇ , generated by the unit matrix: G ⁇ 1 0 ⁇ rec ⁇ ⁇ , (44) ⁇ 0 1 ⁇ ⁇ 170688394.5 Attorney Docket No.: 119314.8121.WO00 [00160]
  • An important example of critically sampled lattice that is not rectangular is the hexagonal lattice ⁇ ⁇ , generated by the basis matrix: G ⁇ a a 2 ⁇ hex ⁇ ⁇ ⁇ , (45) ⁇ 0 a ⁇ 1 ⁇ [00161]
  • the interesting attribute of the hexagonal lattice is that among all critically sampled lattices it has the longest distance between neighboring points.
  • a Zak signal is a function ⁇ :V ⁇ that satisfies the following quasi periodicity condition: ⁇ ⁇ v ⁇ ⁇ ⁇ ⁇ exp ⁇ j 2 ⁇ ⁇ v , ⁇ ⁇ ⁇ ⁇ v ⁇ , (47) [00165] for every v ⁇ V and . r , form: ⁇ ⁇ ⁇ ⁇ k ⁇ r, ⁇ ⁇ l ⁇ r ⁇ ⁇ exp ⁇ j 2 ⁇ k ⁇ r ⁇ ⁇ ⁇ ⁇ , v ⁇ , (48) [00166] that is to say r and quasi-periodic function along the delay dimension with quasi period ⁇ r .
  • the element u acts through two-dimensional shift in combination with modulation by a linear phase.
  • the Heisenberg action simplifies in case the element u belongs to the lattice.
  • the associated with the point ⁇ Consequently, the extended action of an impulse function h ⁇ ⁇ V ⁇ is given by: z . ⁇ , is given by twisted convolution of the impulse h with the waveform ⁇ .
  • the time Zak transform is integration along the Doppler dimension (taking the DC component) for every point of time.
  • the frequency Zak 170688394.5 Attorney Docket No.: 119314.8121.
  • WO00 transform is Fourier transform along the delay dimension.
  • the formulas of the inverse transforms are as follows: ⁇ ⁇ 1 t ⁇ ⁇ ⁇ , ⁇ ⁇ ⁇ ⁇ exp ⁇ ⁇ j 2 ⁇ r n ⁇ ⁇ ⁇ ⁇ n ⁇ r ⁇ , (56) n ⁇ ⁇ [00176] for every and we will denote it by ⁇ ⁇ ⁇ t .
  • P ⁇ 1 ⁇ p ⁇ is given by: P ⁇ , ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ n ⁇ r ⁇ p ⁇ ⁇ ⁇ n ⁇ r ⁇ ⁇ ⁇ [00181]
  • P ⁇ r ⁇ 1 for every a, ⁇ , which means that it is of constant modulo 1 with a regular step function along ⁇ with constant step given by the Doppler coordinate ⁇ .
  • the discontinuity of P as it jumps in phase at every integer point along delay. This phase discontinuity is the Zak domain manifestation of the discontinuity of the rectangular window p at the boundaries.
  • the OTFS transceiver structure depends on the choice of the following parameters: a critically sampled lattice ⁇ ⁇ ⁇ r,0 ⁇ ⁇ ⁇ ⁇ 0, ⁇ r ⁇ , a filter function w ⁇ ⁇ V ⁇ and an 170688394.5 Attorney Docket No.: 119314.8121.WO00 information grid specified by N , M ⁇ .
  • the filter function factorizes as w ⁇ , ⁇ ⁇ w ⁇ ⁇ ⁇ ⁇ w ⁇ ⁇ ⁇ ⁇ where the delay and Doppler factors are square root Nyquist with ⁇ ⁇ ⁇ and ⁇ ⁇ ⁇ r M respectively.
  • the modulated transmit waveform as: ⁇ ⁇ x ⁇ ⁇ ⁇ ⁇ z ⁇ w ⁇ ⁇ ⁇ x ⁇ P ⁇ (61) [00184] To summarize: the information block x 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. [00185] To better understand the structure of the transmit waveform we apply few simple algebraic manipulations to (61).
  • the bare OTFS waveform takes the form: x ⁇ P ⁇ ⁇ ⁇ exp ⁇ j 2 ⁇ m ⁇ K ⁇ n N ⁇ M ⁇ ⁇ ⁇ K ⁇ r ⁇ n ⁇ ⁇ , (64) ⁇ K [00188] In words, of pulse rate ⁇ r ⁇ ⁇ ⁇ 1 r where the shift is determined by the delay parameter n and the modulation is determined Doppler parameter m.
  • V ⁇ 2 be the delay-Doppler plane equipped with the standard symplectic form ⁇ : ⁇ ⁇ v1, v 2 ⁇ ⁇ 1 ⁇ 2 ⁇ ⁇ 2 ⁇ 1 , [00194] for every v1 ⁇ ⁇ ⁇ 1, ⁇ 1 ⁇ and . the polarization form: v 2 ⁇ ⁇ 1 ⁇ 2.
  • ⁇ the symplectic orthogonal complement of ⁇ defined by: ⁇ ⁇ v ⁇ V : ⁇ ⁇ v , ⁇ ⁇ ⁇ for every ⁇ ⁇ , [00199]
  • ⁇ ⁇ ⁇ family of lattices ⁇ ⁇ ⁇ 1 ⁇
  • ⁇ ⁇ ⁇ ⁇ L 2 or, equivalently, the number of points in the quotient group ⁇ / ⁇ ⁇ is equal to we introduce a discrete variant of the twisted convolution operation between functions on the lattice ⁇ .
  • a continuous Zak signal is a function ⁇ :V ⁇ that satisfies the quasi-periodicity condition: ⁇ ⁇ v ⁇ 1 ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ v, ⁇ 1 ⁇ ⁇ ⁇ ⁇ v ⁇ , [00203] for every v ⁇ V and ⁇ 1 ⁇ ⁇ ⁇ , ⁇ ⁇ and ⁇ ⁇ ⁇ k ⁇ , l ⁇ ⁇ then 1 r r the condition takes the form: ⁇ ⁇ ⁇ ⁇ k ⁇ r, ⁇ ⁇ l ⁇ r ⁇ ⁇ ⁇ k ⁇ r , [00204] Given a pair of Zak product as: ⁇ 1 , ⁇ 2 ⁇ ⁇ ⁇ 1 ⁇ v ⁇ ⁇ 2 ⁇ v ⁇ dv , ⁇ [00205] We denote the Hilbert ⁇ ⁇ ⁇ V ⁇ 1, ⁇ ⁇ .
  • the Wigner transform of the rank one operator ⁇ 2 ⁇ 1 is the function ⁇ 1 , ⁇ 2 :V ⁇ given by: ⁇ 1, ⁇ 2 ⁇ v ⁇ ⁇ ⁇ ⁇ v ⁇ ⁇ 1 , ⁇ 2 , [00207] for every v ⁇ V , where ⁇ is called the cross-ambiguity function of the signals ⁇ 1 ⁇ 2 ⁇ , we denote the cross-ambiguity function simply by ⁇ ⁇ and refer to it as the ambiguity function of the signal ⁇ .
  • the conversion between the Zak to the time domain is carried through the Zak transform ⁇ : ⁇ L2 ⁇ t ⁇ ⁇ , given by: ⁇ r ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ , ⁇ ⁇ d ⁇ , 0 170688394.5 Attorney Docket No.: 119314.8121.WO00 [00208] for every ⁇ .
  • ⁇ n , m be the unique quasi-periodic extension of the delta function supported on the ⁇ n ⁇ , m ⁇ ⁇ ⁇ , for 0 ⁇ n ⁇ N ⁇ 1 and 0 ⁇ m ⁇ M ⁇ 1 , i.e.,: ⁇ n , m ⁇ ⁇ ⁇ ⁇ m ⁇ ⁇ ⁇ k ⁇ r ⁇ ⁇ ⁇ n ⁇ ⁇ ⁇ k ⁇ r , m ⁇ ⁇ ⁇ l ⁇ r ⁇ , l r ⁇ [00209]
  • Direct phase modulated, infinite delta pulse train 802 (see FIG.8), given by: ⁇ ⁇ ⁇ n, m ⁇ ⁇ ⁇ ⁇ ⁇ mk M ⁇ ⁇ ⁇ n ⁇ ⁇ ⁇ k ⁇ r ⁇ , k ⁇ ⁇ [00210] 5.3.3 Discrete [00211] The continuous Zak theory admits a (finite)
  • a discrete Zak signal is a function ⁇ : ⁇ that satisfies the following quasi-periodicity condition: ⁇ ⁇ ⁇ ⁇ ⁇ 1 ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ , ⁇ 1 ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ , [00212] for every ⁇ ⁇ and ⁇ n ⁇ ⁇ , m ⁇ ⁇ ⁇ and ⁇ 1 ⁇ ⁇ k ⁇ r , l ⁇ r ⁇ then the condition takes the form: ⁇ ⁇ n ⁇ ⁇ k ⁇ r , m ⁇ ⁇ ⁇ l ⁇ r ⁇ ⁇ ⁇ mk ⁇ ⁇ r ⁇ ⁇ ⁇ n ⁇ ⁇ , m ⁇ ⁇ ⁇ ⁇ [00213] Given as: ⁇ 1 , ⁇ 2 L ⁇ 1 ⁇
  • the discrete Wigner transform of the rank one operator ⁇ 2 ⁇ 1 is the function ⁇ ⁇ given by: ⁇ 1, ⁇ 2 ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ 1 , ⁇ 2 L , [00216] for every ⁇ ⁇ , where is called the discrete cross- ambiguity function of the signals ⁇ 1 and L( ⁇ ⁇ ) ⁇ ⁇ L ⁇ ⁇ ⁇ for every ⁇ ⁇ and ⁇ ⁇ , it follows that ⁇ 1, ⁇ 2 with respect to the sub-lattice ⁇ ⁇ , i.e.,: ⁇ 1, ⁇ 2 ( ⁇ ⁇ ⁇ ⁇ ) ⁇ ⁇ ⁇ 1 , ⁇ 2 ⁇ ⁇ ⁇ , [00217] for every ⁇ ⁇ and denote the discrete cross- ambiguity function by ⁇ ⁇ and refer to it as function of ⁇ .
  • the transform ⁇ is called embedding and it sends a discrete function ⁇ : ⁇ to 170688394.5 Attorney Docket No.: 119314.8121.WO00 the generalized function (distribution) on V given by the following super-position of delta functions: ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ , ⁇ ⁇ [00221] The sampling and to induced transforms between the corresponding Hilbert spaces of signals.
  • Such a function takes the form: w ⁇ , ⁇ ⁇ w ⁇ ⁇ ⁇ ⁇ w ⁇ ⁇ ⁇ ⁇ ⁇ , [00226] for every ⁇ , ⁇ ⁇ .
  • the w on a Zak signal ⁇ is carried through the Heisenberg transform, i.e.,: ⁇ w ⁇ ⁇ ⁇ w ⁇ ⁇ ⁇ w ⁇ ⁇ ⁇ ⁇ ⁇ , [00227]
  • the above equation signal and the Heisenberg transform While the relationship is described as a sequence of mathematical steps, in general, 170688394.5 Attorney Docket No.: 119314.8121.WO00 implementations need not explicitly perform these steps, but may use numerical methods to compute end results without having to compute and store any intermediate results.
  • Theorem 5.2 (Main theorem of filter theory). Given a discrete Zak signal ⁇ L and a Heisenberg filter w ⁇ ⁇ V ⁇ , the following relation holds: ⁇ ⁇ w ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ P ⁇ , ⁇ ⁇ function of the waveform ⁇ w is obtained from the ambiguity function of the sequence ⁇ through shaping with a pulse (whose shape depends on the particular value of ⁇ ). a sense, the design of an Radar waveform involves two aspects.
  • the first concerns the design of a finite sequence of a desired discrete ambiguity function and the second concerns the design of a Heisenberg filter w of a desired pulse shape P ⁇ for various values of ⁇ .
  • P ⁇ a desired pulse shape
  • N , M ⁇ are coprime odd integers.
  • FIG.9 is a block diagram of components of an exemplary OTFS communication system 300.
  • the system 300 includes a transmitting device 310 and a receiving device 330.
  • the transmitting device 310 and the receiving device 330 include first and second OTFS transceivers 315-1 and 315-2, respectively.
  • the OTFS transceivers 315-1 and 315-2 communicate, either unidirectionally or bidirectionally, via communication channel 320 in the manner described herein.
  • the system 300 may comprise a wireless communication system
  • the communication channel may comprise a wired communication channel such as, for example, a communication channel within a fiber optic or coaxial cable.
  • the communication channel 320 may include multiple pathways and be characterized by time/frequency selective fading.
  • FIG.10 illustrates components of an exemplary OTFS transceiver 400.
  • the OTFS transceiver 400 can be used as one or both of the exemplary OTFS transceivers 315 illustrated in the communication system 300 of FIG.9.
  • the OTFS transceiver 400 includes a transmitter module 405 that includes a pre-equalizer 410, an OTFS encoder 420 and an OTFS modulator 430.
  • the OTFS transceiver 400 also includes a receiver module 455 that includes a post- equalizer 480, an OTFS decoder 470 and an OTFS demodulator 460.
  • the components of the OTFS transceiver may be implemented in hardware, software, or a combination thereof. The disclosed OTFS methods will be described in view of the various components of the transceiver 400.
  • a method of OTFS communication involves transmitting at least one frame of data ([D]) from the transmitting device 310 to the receiving device 330 through the communication channel 320, such frame of data comprising a matrix of up to N 2 data elements, N being greater than 1.
  • the method comprises convolving, within the OTFS transceiver 315-1, the data elements of the data frame so that the value of each data element, when transmitted, is 170688394.5 Attorney Docket No.: 119314.8121.WO00 spread over a plurality of wireless waveforms, each waveform having a characteristic frequency, and each waveform carrying the convolved results from a plurality of said data elements from the data frame [D].
  • the OTFS transceiver 315-2 receives and deconvolves these wireless waveforms thereby reconstructing a replica of said at least one frame of data [D].
  • the convolution process is such that an arbitrary data element of an arbitrary frame of data ([D]) cannot be guaranteed to be reconstructed with full accuracy until substantially all of these wireless waveforms have been transmitted and received.
  • iterative equalization and decoding of multi-level encoded symbols exchange extrinsic information between the equalizer and the FEC decoder to achieve close to optimal performance, as shown in FIG.11 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.
  • 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.
  • An inverse OTFS transform module 404 may apply inverse OTFS transform and a symbol demapper 406 may recover bits from modulation symbols.
  • the error-rate performance of the scheme 400 may be degraded.
  • One reason for the degradation may be because of the mixture of bits 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.
  • the iterative receiver 550 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.12, allows the equalizer to receive in earlier iterations priors, which are dominant from the constellation symbols point of view and better improve the equalization.
  • 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 170688394.5 Attorney Docket No.: 119314.8121.WO00 met.
  • the received signal may be equalized by the equalizer 402.
  • 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).
  • FIG.13 is a block diagram of an example embodiment of an iterative 2-D equalizer 501.
  • the 2-D Iterative equalizer illustrated in FIG.13, iterates between the 2-D equalizer 503 and the FEC MAP decoder 505, by passing information from one to the other.
  • the MAP decoder After several iterations, the MAP decoder outputs estimation on the information bits.
  • the iteration termination criteria may be based on a total number of iterations, meeting, but not exceeding, a time budget for the iterative process, the improvement in successive iterations falling below a threshold, and so on.
  • a received grid element is denoted by ⁇ , ⁇ , where ⁇ ⁇ 0,1, ... , ⁇ ⁇ 1 and ⁇ ⁇ 0,1, , ... , ⁇ ⁇ 1.
  • the channel estimation module extracts the channel response h, from the channel estimation area in the delay-Doppler grid.
  • 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, ⁇ ⁇ ⁇ ⁇ .
  • LLRs Log-Likelihoods Ratios
  • 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.
  • 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, 170688394.5 Attorney Docket No.: 119314.8121.WO00 ⁇ ⁇ ⁇ , 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. [00258] If the transmission processing was based on MLC, the basic iterative decoder is modified to accommodate it as well, as illustrated in FIGS.12 and 15.
  • FIGS.11 and 14 show examples of iterative decoder architectures for a single FEC.
  • FIGS.12 and 15 show examples of iterative decoder architectures for multi-level coding (MLC) FEC.
  • the transmitter may allocate a unique pilot symbol in the channel estimation area of the delay-Doppler grid, at location ⁇ ⁇ , ⁇ ⁇ ⁇ .
  • this pilot symbol will be convolved with the channel response and thus allow computing it from the received delay-Doppler grid elements, ⁇ .
  • ⁇ ′ be the received delay-Doppler grid elements, at the channel estimation area (or some part of this area) and zero otherwise, cyclically shifted to the location of the pilot.
  • ⁇ ⁇ ⁇ , ⁇ , ... ⁇ ⁇ ⁇ , ⁇ , ⁇ , ... ⁇ be a set indexes in the delay-Doppler grid of ⁇ ⁇ , which satisfy:
  • the channel response, h is a vector of these received values: h ⁇ ⁇ h ⁇ ⁇ ,h ⁇ , ... , h
  • FIG.16 is an illustration of the channel equation.
  • the a posteriori probability equalizer computes for each delay-Doppler data symbol, ⁇ ⁇ ⁇ , ⁇ ⁇ , the estimated symbol probabilities ⁇ , ⁇ ⁇ Pr ⁇ , ⁇ ⁇ ⁇
  • ⁇ is the set of symbol constellation points of which the symbols were selected at the transmitter and ⁇ ⁇ ⁇ .
  • the a posteriori probability can be also computed and approximated as ⁇ ⁇ , ⁇ ⁇ Pr ⁇
  • the extrinsic LLRs of symbol ⁇ , ⁇ are computed as ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ , ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ log , ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ does the inverse permutation of the interleaver. These modules are optional.
  • FEC Forward error correction
  • the FEC decoder may also be an iterative decoder for codes such as low-density parity check (LDPC) codes or Turbo codes.
  • the symbol mapper converts the coded bits LLRs, computed by the FEC, ⁇ ⁇ , to constellation symbols probability vectors, ⁇ , ⁇ , where its ⁇ -th element ( ⁇ ⁇ 0,1, ... ,
  • the guard area will be as small as possible.
  • the following method allows using a smaller guard area, while refining the channel estimation through the decoder iterations, by removing interference from data symbols that have already been estimated.
  • the symbol mapper output probabilities for the data symbols, ⁇ ⁇ ⁇ ⁇ ⁇ , ⁇ ⁇ is fed to the channel estimation module as well.
  • FIG. 18 depicts a transmitter example, with two antenna ports.
  • Two different streams of delay-Doppler symbols, x ⁇ and x ⁇ are mapped to two delay-Doppler grids, leaving the channel estimation area empty, except for a pilot symbol.
  • the pilot symbols are separated enough, that the channel response from each one of them does not overlap.
  • the receiver may have a delay-Doppler grid for each receive antenna port, ⁇ ⁇ , ⁇ , ... , ⁇ .
  • Two modules are modified to accommodate MIMO: Channel estimation [00293] 6.5.1 MIMO channel estimation [00294]
  • Channel response vectors are derived similarly to the SISO case, for each combination o f transmit and receive antenna.
  • the channel equation can be written in a matrix format: ⁇ ⁇ ⁇ ⁇ , ⁇ ⁇ ⁇ ⁇ ⁇ [00295] or in a ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ [00296] where, ⁇ ⁇ and ⁇ , ⁇ h′ ⁇ , ⁇ ⁇ , ⁇ ⁇ ⁇ ⁇ ⁇ , ⁇ h ⁇ ⁇ ⁇ ⁇ ⁇ [00297] 6.5.2 MIMO [00298]
  • the A Posteriori probability equation changes to a matrix form: ⁇ ⁇ , ⁇ ⁇ Pr ⁇ , ⁇ ⁇ ⁇
  • ⁇ ⁇ ⁇ is the set of symbol constellation points of which ⁇ ⁇ data symbols were selected at the transmitter, for each delay-Doppler grid element and ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ .
  • the a priori and a posteriori probability, ⁇ and ⁇ ⁇ ⁇ also use a matrix notation.
  • An example, for a MIMO MAP equalizer, using an iterative message-passing approach can be found in existing implementations (e.g., Ramachandran et al. “MIMO-OTFS in High-Doppler Fading Channels: Signal Detection and Channel Estimation”).
  • 7.1 OTFS Waveform - Pulse-tones [00301] 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.
  • the 170688394.5 typically quadrature amplitude modulation QAM
  • the 170688394.5 Attorney Docket No.: 119314.8121.
  • WO00 grid may include pilot symbols used for channel detection and estimation.
  • An OTFS waveform can be generated using pre-defined basis signals called Pulsones.
  • the OTFS waveform in the time domain can be considered to be a super-position of pulse-tones multiplied by the grid elements ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ , ⁇ ⁇ ⁇ , ⁇ [00303] where ⁇ , ⁇ are tone is defined as ⁇ ⁇ , ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ [00304] where a operation, ⁇ ⁇ F ⁇ is the inverse Fourier transform of a pulse in the Doppler domain, ⁇ ⁇ ⁇ / ⁇ and ⁇ ⁇ ⁇ / ⁇ are the delay and Doppler grid resolutions, respectively, and ⁇ is the Dirac delta function.
  • the pulse-tones can be considered to be basis signals used for the delay-Doppler grid.
  • a pulse-tone is depicted in FIG.19.
  • This OTFS waveform carrier has the mathematical properties of invariance under time, delay and Doppler shifts. That is, the pulse-tone can remain invariant under the operations of time, delay and Doppler shift. Because of the invariance, when modeling different wireless channels, the underlying coefficients representing the channel remain stable.
  • FIG.20 depicts a visual mathematical example of a pulse-tone as a delay- Doppler domain waveform that is invariant under the Heisenberg uncertainty principle as depicted in FIG.21. The pulse is mathematically quasi-periodic as depicted along the delay and Doppler axes.
  • FIG.22 shows an illustrative representation of a quasi-periodic pulse in the delay- Doppler domain.
  • FIG.23 shows an example of a quasi-periodic pulse with invariance under the Heisenberg uncertainty principle [HUP] within a region defined by the delay period [ ⁇ ⁇ ⁇ and the Doppler period [ ⁇ ⁇ ⁇ as shown [e.g., quasi-periodic pulse – work around HUP].
  • FIG.24 depicts the operation of a Zak transform based implementation in which a pulse-tone is modeled as a time domain pulse realization of a quasi-periodic pulse in the delay-Doppler domain.
  • FIG.25 shows an example representation of a communication using pulse-tones within a region defined by the delay period [ ⁇ ⁇ ⁇ and the Doppler period [ ⁇ ⁇ ⁇ (e.g., crystalline regime).
  • FIG.26 shows a period curve with a depiction of a crystalline regime along the delay-Doppler two dimensional plane where pulse-tone based communication proves to be an efficient 170688394.5 Attorney Docket No.: 119314.8121.WO00 communication technique.
  • the crystalline regime can be the optimal regime for communication and Radar applications.
  • FIG.27 shows the following three fundamental signal representations of time, frequency, and delay-Doppler and example transforms such as Zak transforms to go from one to another.
  • the complexity of the Zak transform is half the complexity of the FFT.
  • 7.2 OTFS Waveform – Crystalline regime [00308]
  • FIG.28 shows examples of channel coupling in the TDM and FDM regimes. The coupling of the channel and the waveform in the TDM and FDM regimes is selective (i.e., fading and unpredictable).
  • FIG.29 depicts examples of channel coupling in the crystalline regime in which delay spread is less than a delay period, ⁇ ⁇ 1/ ⁇ , and Doppler spread is less than a Doppler period, ⁇ , typically satisfying ⁇ ⁇ 2 ⁇ ⁇ , where ⁇ is the maximum expected Doppler shift.
  • ⁇ 500 ⁇ ⁇ ⁇ ⁇ 20 ⁇ and ⁇ ⁇ 5 ⁇ ⁇ ⁇ ⁇ 50 ⁇ .
  • the crystalline regime is between the TDM regime and the FDM regime. In the crystalline regime the channel coupling of the doubly spread channel with the OTFS waveform crystallizes – i.e., predictable and non-fading.
  • the coupling of the channel and the waveform in the TDM/FDM regime is selective – fading and unpredictable.
  • Aliasing which causes time selectivity in the TDM regime and frequency selectivity in the FDM regime, is the root cause. Fading and unpredictability occur in regions of self interaction as illustrated in FIG.30 and FIG.31. When the crystallization condition holds, there is no self interaction.
  • the effects of aliasing is the corruption of communication signals, which are corrected in the crystalline regime. That is, the optimal regime for communication is the crystalline regime, shown in FIG.32, where the channel coupling crystallizes and is predictable and non-fading.
  • OTFS in the crystalline regime is advantageous as superior BER performance is achievable under perfect CSI and under non-perfect CSI (i.e., under model-free mode of operation). Also, within the crystalline regime, OTFS is optimal for Radar sensing as high resolution detection of the delay-Doppler characteristics of reflectors can be achieved with no ambiguity. An example of Radar sensing in the crystalline regime is shown in FIG.33. Additionally, within the crystalline regime, OTFS is optimal for joint communication and sensing with a pair of unbiased pulse-tones (e.g., a Crystaline rotated pulse-tone and a standard crystalline standard pulse-tone) as depicted in FIG.34, allowing simultaneous high communication throughput and high resolution sensing.
  • a pair of unbiased pulse-tones e.g., a Crystaline rotated pulse-tone and a standard crystalline standard pulse-tone
  • an information signal e.g., information bits
  • a crystalline standard pulse- tone to a generate a first signal component.
  • the first signal component can then be summed 170688394.5 Attorney Docket No.: 119314.8121.WO00 (e.g., combined/added) together with a second signal component comprising a crystalline rotated pulse-tone to generate a signal to be transmitted over a channel.
  • the pair of crystalline standard pulse-tone and crystalline rotated pulse-tone are unbiased.
  • the signal transmitted over the channel can be provided as an input to an interference subtraction unit and as an input to a radar sensing unit.
  • the radar sensing unit can then output a radar image and also send the radar image to the interference subtraction unit.
  • the crystalline rotated pulse-tone can also be provided as an input to the interference subtraction unit. With the crystalline rotated pulse-tone, the radar image, and the signal transmitted over the channel provided as inputs to the interference subtraction unit, the interference subtraction unit can provide an output signal to a data detection unit that will then output the information signal (e.g., the information bits).
  • the information signal e.g., the information bits.
  • FIG.35 shows one example embodiment (on transmitter side) for adding pilot signals to a transmission waveform.
  • An information signal may be generated in a delay-Doppler domain (e.g., as QAM or QPSK symbol array).
  • a reference signal e.g., Ref. Signal (ROM/Gen.) x rs [m,n]
  • ROM/Gen. Ref. Signal
  • x rs [m,n] may be added to the information signal [e.g., Information DD x[m,n]] in the delay- Doppler domain, represented by the summation (sigma) block in FIG.35.
  • the resulting signal may be transformed into a time domain signal s(t) using one of several techniques to achieve an OTFS transformation of the signal.
  • FIG.36 shows another arrangement (on transmitter side) for adding a reference signal (e.g., Ref. Signal (ROM/Gen.) to the information signal (e.g.,, x[m,n]) to generate a transmission waveform s(t).
  • a reference signal e.g., Ref. Signal (ROM/Gen.
  • the information signal e.g., an array of symbols
  • the reference signal may be added to the resulting signal in the time domain to generate the transmission waveform s(t).
  • the reference signal may be generated in real-time using a waveform generator or may be pre-stored in a memory and read back during the process of combining with the information signal.
  • the reference signal may have the following properties: [00316] [1] The reference signal spreads over the entire ⁇ ⁇ ⁇ delay-Doppler grid. 170688394.5 Attorney Docket No.: 119314.8121.WO00 [00317] [2] Super-imposed over the data. [00318] [3] Satisfies: [00319] ⁇ , ⁇ ⁇ ⁇ ⁇ ⁇ , ⁇ ⁇ ⁇ ⁇ ⁇ reference signal after the OTFS transform.
  • FIG.37 pictorially depicts an example of effect of a transmission channel on a transmitted signal.
  • the depicted example shows a two-path channel (e.g., two discrete paths in the channel).
  • the grid shows a grid in a two-dimensional domain (e.g., delay-Doppler) with the top-left position showing identity (no distortion) coefficient.
  • two coefficients represent the distortion caused by the channel... h[1,1] and h[3,2].
  • the reference signal contribution at the [3,2] location comes from the reference signal at the [0, 0] location due to the operation of h[1,1] and h[3,2].
  • a receiver-side implementation can perform channel estimation by cross- correlating the received signal (with an underlying delay-Doppler domain representation) with a conjugate of the known reference signal to obtain an estimated channel response at coordinates [k,l].
  • the phase in the equation below may be used to compensate for the channel response rotation as a function of delay-Doppler coordinates.
  • For side can include cross correlating a received delay-Doppler data, ⁇ , ⁇ , with the conjugate of a known transmitted reference signal ⁇ ⁇ ⁇ , ⁇ ⁇ ⁇ , to obtain the estimated channel response at delay-Doppler coordinates ⁇ , ⁇ ; 170688394.5 Attorney Docket No.: 119314.8121.WO00 and the additional phase can be used to compensate for the channel response rotation as a function of the delay-Doppler coordinates.
  • FIG.38 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 one or more processors 802, a memory 804 (this may be optional and in some cases the memory may be internal to the processor) and at least one transceiver circuitry 806.
  • the processor may execute instructions, e.
  • the memory 804 and/or the transceiver circuitry 806 may be partially or completely contained within the processor(s) 802 (e.g., same semiconductor package).
  • the following solutions may be preferably implemented by some embodiments.
  • some solutions may be as follows. [00333] 1.
  • a method of transmitting a signal comprising: generating (902) a two-dimensional delay-Doppler signal comprising a sum of an information signal and a reference signal, wherein the sum is performed in delay-Doppler domain; and generating (904) a transmission waveform from the two-dimensional delay-Doppler signal.
  • a transmission waveform is generated by performing an orthogonal time frequency space transform (OTFS) on the two-dimensional delay-Doppler signal.
  • OTFS orthogonal time frequency space transform
  • the OTFS transform comprises a forward or an inverse symplectic Fourier transform.
  • the method of solution 1, wherein the transmission waveform is generated by applying a Zak transform. [00337] 5. The method of solution 1, wherein the transmission waveform is generated by applying a two-dimensional transform. [00338] 6. The method of solution 1, wherein the transmission waveform is generated by applying a pulse-tone waveform in the delay-Doppler domain. [00339] 7. The method of solution 6, wherein the pulse-tone waveform comprises a quasi- periodic pulse. 170688394.5 Attorney Docket No.: 119314.8121.WO00 [00340] 8.
  • a method of transmitting a signal comprising: generating (912) a transmission waveform as a summation of a first signal component and a second signal component, wherein the sum is performed in a time domain; wherein the first signal component comprises a reference signal, wherein the second signal component is generated by transforming a two-dimensional information signal from a delay- Doppler domain to a time domain.
  • the second signal component is generated by performing an orthogonal time frequency space (OTFS) transform.
  • OTFS orthogonal time frequency space
  • the method of solution 10, wherein the second signal component is generated by applying a two-dimensional transform. [00347] 14. The method of solution 10, wherein the second signal component is generated by applying a pulse-tone waveform in the delay-Doppler domain. [00348] 15. The method of solution 14, wherein the pulse-tone waveform comprises a quasi- periodic pulse. [00349] 16. The method of solution 14, wherein the pulse-tone waveform is implemented in a portion of the delay-Doppler domain where a delay spread is less than a delay period and a Doppler spread is less than a Doppler period. [00350] 17.
  • a method implemented at a receiver-side comprising: receiving (922) a received signal over a transmission channel, determining (924), by processing the received signal in a delay-Doppler domain, an estimate of cross-correlation between the received signal and a known reference signal that makes up the received signal, 170688394.5 Attorney Docket No.: 119314.8121.WO00 and estimating (926) a delay-Doppler domain channel characteristic of the transmission channel based on the estimate of cross-correlation.
  • a method of transmitting a signal (e.g., method 930 depicted in FIG.39D), comprising: generating (932) a transmission waveform as a summation of a first signal component and a second signal component, wherein the first signal component comprises an information signal modulated with a standard pulse-tone, and wherein the second signal component comprises a rotated pulse-tone.
  • a transmission waveform as a summation of a first signal component and a second signal component, wherein the first signal component comprises an information signal modulated with a standard pulse-tone, and wherein the second signal component comprises a rotated pulse-tone.
  • a digital communication apparatus comprising one or more processor electronics and one or more transceiver electronics, wherein the transceiver is configured to receive or transmit a signal under control of the one or more processor electronics, and wherein the one or more processor electronics is configured to implement a method recited in any of solutions 1 to 22.
  • the hardware platform disclosed in FIG.38 may be used for the implementation of the above methods.
  • [00358] 24. A computer-readable storage medium having code stored thereon, the code, upon execution by one or more processors, causing the one or more processors to implement a method recited in any one or more of solutions 1-22.
  • OTFS operation in the crystalline regime can be advantageous for various communication applications such as Radar sensing and simultaneous joint communication and sensing applications as high communication throughput and high resolution 170688394.5 Attorney Docket No.: 119314.8121.
  • WO00 sensing/detection can be achieved in the crystalline regime where non-fading and predictability of the channel may be improved.
  • OTFS is a universal family of waveforms admitting TDM and FDM as limits.
  • the present document further discloses operational trade- offs and design choices available to implementors of OTFS technology.
  • crystalline regime is introduced.
  • OTFS is optimal for communication, the channel coupling crystallizes – becoming non-fading and predictable.
  • Theory and simulations demonstrate superior performance under perfect CSI and superior performance under non-perfect CSI (Model free).
  • OTFS is optimal for Radar sensing.
  • the disclosed waveform facilitate high resolution detection of delay-Doppler characteristics of the reflectors, with no (or suppressed) ambiguity.
  • OTFS is optimal for joint communication and sensing, e.g., using a pair of unbiased Pulsones (or pulse- tones) and provides simultaneous high communication throughput and high-resolution sensing.
  • 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.
  • 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.
  • 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. 170688394.5 Attorney Docket No.: 119314.8121.WO00 [00364]
  • a computer program also known as a program, software, software application, script, or code
  • 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.
  • 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.
  • 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.
  • 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.
  • mass storage devices for storing data
  • 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.

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  • Engineering & Computer Science (AREA)
  • Signal Processing (AREA)
  • Computer Networks & Wireless Communication (AREA)
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  • Discrete Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Cable Transmission Systems, Equalization Of Radio And Reduction Of Echo (AREA)

Abstract

Un procédé mis en œuvre au niveau d'un côté récepteur dans un réseau de communication numérique comprend la réception d'un signal reçu sur un canal de transmission, la détermination, par traitement du signal reçu dans un domaine retard-Doppler, d'une estimation de corrélation croisée entre le signal reçu et un signal de référence connu qui constitue le signal reçu, et l'estimation d'une caractéristique de canal de domaine de retard-Doppler du canal de transmission sur la base de l'estimation de corrélation croisée.
PCT/US2025/014206 2024-02-01 2025-01-31 Traitement de signal pilote dans le domaine retard-doppler Pending WO2025166301A1 (fr)

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US20200322185A1 (en) * 2016-05-20 2020-10-08 Cohere Technologies Iterative channel estimation and equalization with superimposed reference signals
US20210250138A1 (en) * 2018-06-14 2021-08-12 Cohere Technologies, Inc. Co-existence of orthogonal time frequency space and long term evolution systems
WO2023028601A1 (fr) * 2021-08-26 2023-03-02 Cohere Technologies, Inc. Mise en forme d'impulsion dans le domaine retard-doppler
US20230224115A1 (en) * 2020-09-04 2023-07-13 Vivo Mobile Communication Co.,Ltd. Pilot Reception Processing Method, Pilot Transmission Method, and Related Device

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US20200322185A1 (en) * 2016-05-20 2020-10-08 Cohere Technologies Iterative channel estimation and equalization with superimposed reference signals
US20210250138A1 (en) * 2018-06-14 2021-08-12 Cohere Technologies, Inc. Co-existence of orthogonal time frequency space and long term evolution systems
US20230224115A1 (en) * 2020-09-04 2023-07-13 Vivo Mobile Communication Co.,Ltd. Pilot Reception Processing Method, Pilot Transmission Method, and Related Device
WO2023028601A1 (fr) * 2021-08-26 2023-03-02 Cohere Technologies, Inc. Mise en forme d'impulsion dans le domaine retard-doppler

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