Channel sensing using pulse-tone signals

Abstract

Channel sensing is performed using one or more signal transmissions that are included in gaps (e.g., inter-tile spacings or inter-frame spacings) separating data frame transmissions in a digital communication system. The signal transmissions comprise pulse-tone signals that are invariant under time, delay and Doppler shifts. The number of channel sensing signal transmissions performed within a gap and in all gaps within a frame are a function of an expected maximum delay spread or an expected maximum Doppler spread among all the channels that are being sensed. An example transmitter is configured to perform a channel sensing signal transmission, and sense a channel using feedback received based on the channel sensing signal transmission. An example receiver is configured to receive a channel sensing signal, and provide feedback. An example user-device is configured to use one or more channel parameters in the feedback to configure a transceiver for subsequent communications.

Description

International Patent Application 119314.8125.WO00 CHANNEL SENSING USING PULSE-TONE SIGNALS CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application is a continuation and claims priority to U.S. Provisional Application No. 63 / 671,630, filed on July 15, 2024, the disclosure of which is hereby incorporated by reference herein in its entirety. TECHNICAL FIELD

[0002] The present document relates to digital communication. BACKGROUND

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

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

[0005] This document discloses techniques that may be adopted by systems that use transmission waveforms based on orthogonal time frequency space (OTFS) modulation technology. In particular, using the disclosed techniques, channel sensing may be performed.

[0006] In an example aspect, a digital communication method includes performing, for multiple users, a plurality of channel sensing signal transmissions using transmission resources in a plurality of inter-tile spacings separating resource tiles in a two-dimensional resource plane, and receiving, for each of at least two users of the multiple users, one or more parameters associated with a resource tile allocated to a corresponding user. Herein, the plurality of channel sensing signal transmissions comprises signal waveforms determined using basis functions that are invariant under operations of time, delay, and Doppler shift. 182120091.2International Patent Application 119314.8125.WO00

[0007] In another example aspect, another digital communication method includes receiving, multiple users, a plurality of channel sensing signal transmissions on transmission resources in a plurality of inter-tile spacings separating resource tiles in a two-dimensional resource plane. The method further includes determining, based on the plurality of channel sensing signal transmissions, one or more parameters associated with a resource tile allocated to each of at least two users of the multiple users, and transmitting the one or more parameters corresponding to the at least two users. Herein, the plurality of channel sensing signal transmissions comprises signal waveforms determined using basis functions that are invariant under operations of time, delay, and Doppler shift.

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

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

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

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

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

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

[0014] FIG.3 shows an example of an infinite delta train, with rotating phases, multiplied by a truncated time window.

[0015] FIGS.4A and 4B show example pulses used as basis signals for wireless communication.

[0016] FIG.4C shows an example of rotations undergone by a delay-Doppler domain pulse.

[0017] FIG.5 is an example of a quasi-periodic delay Doppler domain pulse.

[0018] FIG.6 depicts an example of channel distortions undergone by a pilot signal. 182120091.2International Patent Application 119314.8125.WO00

[0019] FIG.7 is a block diagram of an example of a Zak transform based wireless system that includes a transmitter and a receiver.

[0020] FIG.8 shows an example of the effects of a doubly spread channel.

[0021] FIG.9 shows an example of predictability being achieved in the crystalline region.

[0022] FIG.10 is a block diagram of an example of a transmitter.

[0023] FIG.11 shows an example of a Zak-OTFS carrier waveform.

[0024] FIG.12 shows an example of Zak-OTFS transceiver processing.

[0025] FIG.13 is a block diagram of an embodiment of signal generation.

[0026] FIG.14 is a block diagram of another embodiment of signal generation.

[0027] FIG.15 is a block diagram of another embodiment of signal generation.

[0028] FIG.16 shows an example of allocation of OTFS frames and physical resource blocks (PRBs) within a 1 ms time interval across various bandwidths and grid configurations.

[0029] FIG.17 shows examples of frame allocation based on the number of subcarriers and bandwidth, which affect complexity considerations, for different OTFS frame configurations.

[0030] FIG.18 shows another example of OTFS frame and PRB allocation for different bandwidths and subcarrier spacings within a 1 ms time interval.

[0031] FIG.19 shows the mapping of PRBs in the time-frequency plane, and the delay and Doppler dimensions for OTFS frame tiling.

[0032] FIG.20 shows an expanded view of delay-Doppler domain organization, highlighting frequency domain units and subcarrier spacing.

[0033] FIG.21 shows an example of PRB tiling in the time-frequency domain for different time and frequency resource units.

[0034] FIG.22 shows an example of tiling PRBs along the delay-Doppler axis for multi-user access.

[0035] FIG.23 shows an example arrangement of PRBs with guard bands along delay-Doppler two-dimensional plane.

[0036] FIG.24 shows examples of PRB time-frequency tiling options.

[0037] FIG.25 shows an example of latency-based PRB tiling.

[0038] FIG.26 shows an example of inserting sensing signals in inter-frame spacings. 182120091.2International Patent Application 119314.8125.WO00

[0039] FIG.27 shows another example of sensing signals being positioned within the time- frequency 2D resource plane with different periodicities.

[0040] FIG.28 shows another example of sensing signals being positioned within the time- frequency 2D resource plane.

[0041] FIG.29 shows a numerical example of sensing signals in the 2D resource plane.

[0042] FIG.30 shows another numerical example of sensing signals in the 2D resource plane.

[0043] FIG.31 shows an example of multiplexing signals in the 2D resource plane.

[0044] FIG.32 shows an example implementation of inserting sensing signals in gaps.

[0045] FIG.33 shows an example signal transmission arrangement.

[0046] FIG.34 shows an example of pulse-tone sensing signals for different users.

[0047] FIG.35 shows the concept of pulse-tone sensing signals for different users.

[0048] FIG.36 shows an example of signal processing for oversampling the channel for sensing.

[0049] FIGS.37-39 show examples of different arrangements of frames and tiles in the 2D time- frequency resource plane.

[0050] FIG.40 shows an example of the relationship between PRBs and subbands.

[0051] FIG.41 shows an example of a timing relationship between pulse-tone signals and sensing windows.

[0052] FIG.42 shows an example arrangement of sensing signal transmissions based on delay spread.

[0053] FIG.43 shows details of an example OTFS waveform.

[0054] FIG.44 shows an example of digital communication processing using the Zak transform.

[0055] FIG.45 shows examples of sensing signals and scaling periodicities based on resource plane configurations.

[0056] FIG.46 shows an example of a resource plane in which the one or more gaps are allocated for transmission of sensing signals.

[0057] FIGS.47 and 48 are flowcharts showing example methods of digital communication.

[0058] FIG.49 shows an example of a hardware platform. DETAILED DESCRIPTION

[0059] To make the purposes, technical solutions and advantages of this disclosure more apparent, various embodiments are described in detail below with reference to the drawings. 182120091.2International Patent Application 119314.8125.WO00 Unless otherwise noted, embodiments and features in embodiments of the present document may be combined with each other.

[0060] Section headings are used in the present document to improve readability of the description and do not in any way limit the discussion or the embodiments to the respective sections only. Furthermore, certain standard-specific terms are used for illustrative purposes only, and the disclosed techniques are applicable to any wireless communication systems.

[0061] 1 Introduction – Examples of wireless communication environments

[0062] The wireless or time-variant nature of the communication channel poses several challenges in design a transmission protocol suitable for wireless communication scenarios. These days, users expect their wireless devices to work everywhere and in a variety of mobile or stationary situations.

[0063] The relative movement of transmitters and receivers with respect to each other cause signal distortions such as varying channel delay, Doppler and / or angular spread, signal degradation due to ground clutter, sea clutter, and so on. Another example of signal degradation is flat fading in which an entire channel occupied by a transmission signal will experience fading or attenuation that may be relatively constant across the channel. In practice, a transmission scheme may need to be designed to fit within a certain link budget, maximum power constraint, or linearity of electronics used for transmitting or receiving signals.

[0064] 2 Example wireless systems

[0065] FIG.1 shows an example of a wireless communication system 100 in which a transmitter device 102 transmits signals to a receiver 104. The signals may undergo various wireless channels and multipaths, as depicted. Some reflectors such as buildings and trees may be static, while others such as cars, may be moving scatterers. The transmitter device 102 may be, for example, a user device, a mobile phone, a tablet, a computer, or another Internet of Things (IoT) device such as a smartwatch, a camera, and so on. The receiver device 104 may be a network device such as the base station. The signals transmitted from the base station to the transmitter 102 may experience similar channel degradations produced by static or moving scatterers. The techniques described in the present document may be implemented by the devices in the wireless communication system 100. The terms “transmitter” and “receiver” are simply used for convenience of explanation. As further described herein, depending on the direction of 182120091.2International Patent Application 119314.8125.WO00 transmission (uplink or downlink), the network station may be transmitting or receiving and user device may be receiving or transmitting.

[0066] FIG.2 shows a simplified wireless network to highlight certain aspects of the disclosed technology. A transmitter transmits wireless signals to a receiver in the wireless network. Some transmissions in the network, variously called downlink or downstream transmissions, a network-side node such as a base station acts as a transmitter of wireless signals and one or more user devices act as the receiver of these wireless signals. For some other transmissions, as depicted in FIG.2, the direction of transmission may be reversed. Such transmissions are often called uplink or upstream transmissions. For such transmissions, one or more user devices act as transmitters of the wireless signals and a network-side node such as the base station acts as the receiver of these signals (as depicted in FIG.2). Other types of transmissions in the network may include device-to-device transmissions, sometimes called direct or sideband transmissions. While the present document primarily uses the terms “downlink” and “uplink” for the sake of convenience, similar techniques may also be used for other situations in which transmissions in two directions are performed - e.g., inbound or incoming transmissions that are received by a wireless device and outbound or outgoing transmissions that are transmitted by a wireless device. For example, downlink transmissions may be inbound transmissions for a user device, while outbound transmissions for a network device. Similarly, uplink transmissions may be inbound transmissions for a network device while outbound transmissions from a wireless device. Therefore, for some embodiments, the disclosed techniques may also be described using terms such as “inbound” and “outbound” transmission without importing any 3GPP-specific or other wireless protocol-specific meaning to the terms “uplink” and “downlink.”

[0067] In frequency division multiplexing (FDM) networks, the transmissions to a base station and the transmissions from the base station may occupy different frequency bands (each of which may occupy continuous or discontinuous spectrum). In time division multiplexing (TDM) networks, the transmissions to a base station and the transmissions from the base station occupy a same frequency band but are separated in time domain using a TDM mechanism such as time slot-based transmissions. 182120091.2International Patent Application 119314.8125.WO00

[0068] 3 Overview of OTFS waveforms and basis functions

[0069] 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 delayperiod, ^^^ ൌ 1 / ^^^. The grid has ^^ ^ ^^^^ ∙ ^^^ elements along Doppler and ^^ ^ ^^^^ ∙ ^^^^^elements along delay, where ^^^^ isof the OTFS signal and ^^ is its duration. On top of the information bearing symbols (typically quadrature amplitude modulation QAM), the grid may include pilot symbols used for channel detection and estimation.

[0070] The OTFS waveform in the time domain, may be considered to be a super-position of pulse tone signals (e.g., Pulsones™ waveforms) multiplied by the grid elements ேି^ ெି^ ^^^^^^ ^ ^ ∙ ^^^^,^^^^^^(1)

[0071] where ^^^^^,^^^are^^^^,^^^^^^ ≜ ^^ ∗ ∙ ^ ^^^ଶగ^∆ఔ^ ^^Δ^^(2)

[0072] ^^௧^^^^ ൌ ℱି^^^^ఔ^ is the inverse Fourier transform of a pulse in the Doppler domain, Δ^^ ൌ ^^^ / ^^and ∆^^ ൌ ^^^ / ^^are the delay and Doppler grid resolutions, respectively, and ^^^∙^ is the Diracdelta function. In general, the Pulsones may be considered to be basis signals used for the delay- Doppler grid.

[0073] In this document, we will use the notation ∆^^,^^^ ^^^^ for the second term of (2), which represents an infinite delta train, with rotating multiplied by a time window:^ ∆^^,^^^ ^^^^ ≜ ^^ ^^^^ ∙ ^ ^^^ଶగ^∆ఔ^ఛ^^^൫^^ െ ^^Δ^^ െ ^^^^^൯(3)

[0074] In tothe effective as

[0075] 3.1 Examples of pulse-tone waveforms

[0076] FIGS.4A and 4B show examples of pulses that can be used as basis signals for wireless communication. FIG.4A illustrates an example of separating sensing and communication, and 182120091.2International Patent Application 119314.8125.WO00 depicted with a pilot signal (e.g., point pulse-tone x=xs), where the cross-ambiguity can be represented as Ay,x[k,l].

[0077] In some embodiments, separate Zak-OTFS subframes may be dedicated to sensing and data transmission and / or communication. In other embodiments, and as described in this patent document, the data transmissions may be performed in Zak-OTFS subframes (or resource tiles), and the sensing is performed in the inter-subframe spacing (or inter-tile spacing). More generally, the sensing is performed in gaps between allocated resources.

[0078] In these embodiments, a transmitter may transmit a pilot, and the receiver may read off the input / output (I / O) relation for the entire subframe from the response to a single pilot, and then use this estimate to equalize the data in a subsequent data subframe. For example, as depicted in FIG.4A, the discrete I / O can be read off from the response to a single pilot signal transmitted through a linear time variant (LTV) channel, and the channel estimate can be used to recover data in a subsequent Zak-OTFS subframe.

[0079] The described embodiments use linear time invariant (LTI) channel models, as depicted in FIG.4B, where a time-domain (TD) pulse is a geometric mode of the LTI channel – the I / O relation is made up of delays that move the pulse about in time. The I / O relation can be read off from the response to a single TD pulse. After waiting longer than the delay spread, embodiments can read off the I / O relation, and equalize the data. Because delay-Doppler profile of a channel typically is static over long time periods, this approach can provide predictability, which means that the I / O relation does not change with time. And predictability can enable a model-free mode of operation under the condition where delay spread is less than a delay period of the pulse being used as a basis signal.

[0080] FIG.4C is an example of rotations undergone by a delay-Doppler domain pulse. In FIG. 4C, a pulse in the delay-Doppler domain is shown, which can, for example, have a delay spread ^^^= 50 µs and a Doppler spread ^^^= 20 KHz.

[0081] However, defining a pulse in the delay-Doppler (DD) domain is subject to the Heisenberg Uncertainty Principle (HUP), which implies that it is not possible to simultaneously localize a signal in delay and in Doppler. Embodiments of the disclosed technology work around the HUP by starting with a pulse in the DD domain and extending it quasi-periodically. 182120091.2International Patent Application 119314.8125.WO00

[0082] The DD domain pulse can be represented as a configuration of infinitely many pulses which repeat at integer multiples of the delay period ^^^along the delay axis and at integer multiples of the Doppler period ^^^along the Doppler axis. A box of width ^^^and height ^^^isreferred to as the fundamental period, and it is assumed that ^^^^^^ ൌ 1.

[0083] In these examples, the phase of the pulse changes when the pulse location shifts by an integer multiple of ^^^along the delay axis, but there is no change in phase when the pulse location shifts by an integer multiple of ^^^along the Doppler axis. Accordingly, the DD realization of a TD signal is a quasi-periodic function. FIG.5 shows an example of a quasi- periodic delay-Doppler domain pulse.

[0084] A DD domain pulse can be transformed to a TD pulse-tone waveform by applying an (inverse time) Zak transform. That is, an (inverse time) Zak transform may be applied to get a TD pulse-tone from a quasi-periodic DD domain pulse. There is also an inverse (frequency) Zak transform that transforms a DD domain pulse to a frequency-domain (FD) pulse-tone.

[0085] In these examples, a DD domain pulse is located at (^^^, ^^^) within the fundamental period. The DD domain pulse is spread along the delay axis over a length 1 / B (i.e., B−1) and is spread along the Doppler axis over a length 1 / T (i.e., T−1). The TD realization x(t) can be obtained by applying the Zak transform to the DD domain pulse ^^^^^^(^^, ^^). The TD realization x(t) is a pulse train of finite duration T, with each pulse in the train spread over time duration 1 / B. Consecutive pulses of the pulse train are separated by the delay period ^^^– moving the pulse location ^^^along the delay axis displaces the TD pulse-tone in time. The pulse train is modulated by a sinusoid of frequency ^^^– moving the pulse location ^^^along the Doppler axis displaces the modulating tone in frequency.

[0086] Herein, time division multiplexing (TDM) is a limiting case. As the delay period ^^^grows, the TD pulses grow further apart, the tone structure disappears, and only a single TD pulse at ^^^remains. Similarly, frequency division multiplexing (FDM) is also a limiting case. As delay period ^^^shrinks, the pulses grow closer and closer together in time, and in the limit, the pulse structure disappears and only the tone remains. Pulse-tones parametrized by ^^^and ^^^interpolate between TDM and FDM; that is, they live on the hyperbola ^^^^^^ ൌ 1, with aparticular value of ^^^optimizing predictability. 182120091.2International Patent Application 119314.8125.WO00

[0087] Pulse-tones are optimal as time- and band- limited signals because there is almost no overlap between two DD pulses whose delay domain locations differ by 1 / B or whose Doppler locations differ by 1 / T. In the example depicted in FIG.5, B= 1 / 100ns = 10MHz, T = 1 / 1kHz = 1ms, N = 50μs / 100ns = 500, and M = 20kHz / 1kHz = 20, with ^^^= 20 KHz (Doppler spread) and ^^^= 50 ms (delay spread).

[0088] FIG.6 depicts an example of channel distortions undergone by a pilot signal. In this example, the input-output response can be determined using a twisted convolution defined by: ^^(^^,^^)=ℎ(^^, ^^) ∗^^ ^^(^^, ^^), where ℎ^^^, ^^^ ൌ ∑ସ ^ୀ^ ℎ^^^^^^ െ ^^^^^^^^^ െ ^^^^.

[0089] of a doubly spread wireless channel on a pulse-tone to be predictable and geometric. In some examples, “geometric” may mean that for a channel path delay, the DD domain pulse is simply translated along the delay axis by an amount equal to the path delay. Additionally, or alternatively, it may be advantageous that for channel path Doppler shift, the DD domain pulse is simply translated along the Doppler axis by an amount equal to the Doppler shift.

[0090] As discussed above, pulse-tone waveforms live on the hyperbola ^^^^^^ ൌ 1, andaccordingly the action of the doubly spread channel on a pulse-tone is predictable if the fundamental period captures the delay and Doppler spreads of the channel. Herein, the fundamental period captures the channel spreads when the delay domain period ^^^is greater than the channel path delay spread and the Doppler domain period ^^^is greater than the channel path Doppler spread. When these conditions are met, the system is operating in a “crystalline regime” and the action of a doubly spread channel on a pulse-tone is predictable. In some embodiments, such as FIG.6, this can allow the predictability of LTV channels, where wireless channel dynamics can lead to replicas.

[0091] FIG.7 is a block diagram of an example of a Zak transform based wireless system including a transmitter and a receiver. The example Zak transform based wireless system of FIG. 7 supports signal processing in Zak-OTFS. As shown therein, the continuous output is the twisted convolution of the input with the effective DD channel filter. Quasi-periodic signals are shown in gray scale, and the discrete output is obtained by sampling the continuous output on the information grid. Herein, the discrete output is the discrete twisted convolution of the discrete input with the discrete effective DD channel filter. 182120091.2International Patent Application 119314.8125.WO00

[0092] For the example system of FIG.7, the Zak-OTFS I / O relation can be represented as: ^^௪^^ௗௗ ^^^, ^^^ = ^^^௫^^^, ^^^ ∗ఙ ℎ^^^, ^^^ ∗ఙ ^^௧௫^^^, ^^^ ∗ఙ ^^ௗௗ^^^, ^^^ ൌ ℎௗௗ^^^, ^^^ ∗ఙ ^^ௗௗ^^^, ^^^.

[0093] channels acting on pulse-tones). As shown therein, the interaction of a doubly spread channel with a TD pulse-tone is predictable and geometric. In the crystalline regime, the delay domain period ^^^is greater than the channel path delay spread, and the Doppler domain period ^^^is greater than the path Doppler spread, i.e., ^^^> delay spread and ^^^> Doppler spread.

[0094] When communicating with a pulse-tone (e.g., PulsoneTM) in the crystalline regime, the input-output relations can be governed by twisted convolution, in which the I / O relation for the entire subframe can be learned directly, without learning the channel, by reading off the response to a single transmitted pilot. That is, this configuration exploits the fact that unpredictability results from aliasing in the Delay-Doppler domain, which occurs when the channel spreads are bigger than the delay-Doppler periods of the pulse-tone.

[0095] FIG.9 shows an example of predictability being achieved in a crystalline region (or regime) in wireless communications.

[0096] In this example, a doubly spread channel is provided and M=N=4 is fixed to have 16 bins, and the average power of the received discrete DD domain signal for varying ^^^and ^^^isplotted on the hyperbola ^^^^^^ ൌ 1. As the delay domain period shrinks, aliasing in delay andfrequency selectivity in FDM results. Similarly, as the Doppler domain period shrinks, aliasing in Doppler and time selectivity in TDM results. There is a sweet spot in the middle of the hyperbola where the fundamental period can capture the channel spread. When the fundamental period captures the channel spread, there is no fading. Here, the received power profile is flat like the surface of a crystalline solid and this is called the crystalline regime.

[0097] In the crystalline regime, there is no fading and the input-output (I / O) relation is predictable. As described above, DD domain aliasing controls predictability – as the delay domain period shrinks, aliasing in delay and frequency selectivity in FDM results; as the Doppler domain period shrinks, aliasing in Doppler and time selectivity in TDM results; and in the crystalline regime, there is no fading and the input-output (I / O) relation is predictable. 182120091.2International Patent Application 119314.8125.WO00

[0098] 4 Examples of OTFS Transmitters

[0099] In some embodiments, the OTFS transmitter encodes information bits in one or more Forward-Error-Correction (FEC) codes, corresponding to one or more symbol constellation levels (denoted by ^^), interleave the coded bits and map them to symbols (typically QAM) which are then assigned to delay-Doppler grid elements. Some of the delay-Doppler grid elements may not be assigned with any symbols (value of zero) and others may be assigned with known symbols (pilots). Finally, the OTFS modulator is applied to the delay-Doppler grid.

[0100] FIG.10 shows an example of generating an OTFS waveform based on the description above. From left to right, source bits (e.g., data bits) are input to a number of FEC stages, each operating at a corresponding code rate. The FEC coded outputs are interleaved through corresponding interleavers. In some examples, the interleaving operation using corresponding interleavers may be omitted. 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.

[0101] 5 Examples of OTFS Modulators

[0102] The OTFS modulator implements equation (1), generating a time-domain signal ^^^^^^. This equation may be implemented in multiple ways, such as using the Zak transform, a two- dimensional (2D) transform such as a Fast Fourier Transform (FFT) that is a symplectic transform, or using Pulsones™ which are a combination of pulse-tone waveforms.

[0103] 5.1 Example implementations of OTFS waveform generation

[0104] As discussed above, the Zak-OTFS I / O relation is predictable when delay and Doppler periods are greater than the effective channel delay and Doppler spreads, respectively. This condition is referred to as the crystallization condition (or the system operating in the crystalline regime). Herein, the filter taps can be read off from the response to a single Zak-OTFS point (impulse) pulse-tone waveform, and the I / O relation can be reconstructed for a sampled system that operates under finite duration and bandwidth constraints. Predictability opens up the possibility of a model-free mode of operation.

[0105] Furthermore, a time-domain (TD) pulse is an ideal waveform for delay-only channels (where paths induce zero Doppler shift) since it is possible to separate signals received along different paths according to their path length / distance. Similarly, a frequency-domain (FD) pulse 182120091.2International Patent Application 119314.8125.WO00 is an ideal waveform for Doppler-only channels since it is possible to separate signals received along different paths according to the Doppler shift induced on the transmitted signal. However, neither a TD pulse nor a FD pulse is suited for doubly-spread channels where paths induce both delay and Doppler shift.

[0106] To achieve operation in the crystalline regime, embodiments of the disclosed technology match a pulse in the delay-Doppler (DD) domain to doubly-spread channels.

[0107] In some embodiments, a pulse in the DD domain is a quasi-periodic localized functionthat is defined by a delay period ^^^ and a Doppler period ^^^ ൌ 1 / ^^^. In the associated periodlattice Λ^ ൌ ^൫^^^^^, ^^^^^൯|^^, ^^ ∈ ℤ^, there is only one pulse within the fundamental regiondefined

[0108] Furthermore, there aredelay axis and the Doppler axis given by:

[0109] Only quasi- When viewedin the time domain, this function can be realized as a pulse train modulated by a tone (see e.g. FIG. 11), hence the name Pulsone™. The DD domain pulse is the carrier waveform for Zak- OTFS modulation.

[0110] In these described embodiments, Zak-OTFS modulation with modulation parameters (^^^,^^^ ൌ 1 / ^^^) are considered. Herein, the transmitted TD Zak-OTFS frame is limited to a timeduration ^^ ൌ ^^^^^ and bandwidth ^^ ൌ ^^^^^. FIG. 12 shows an example of Zak-OTFS transceiverprocessing.

[0111] Let x ^ k, l ^ , k ^ 0,1,^ , M –1, l ^ 0,1, ^ , N –1 denote the ^^^^ ൌ ^^^^ informationsymbols, each having unit averageMN information symbols are encoded into a discrete DD domain information signal ^^ௗௗ^∙,∙^ given by ^ଶ ^^^^ௗௗ^^^ ^ ^^^^, ^^ ^ ^^^^^ ≡ ^^గே௫^^,^^ (4)

[0112] for all k ^ 0,1,^ ,182120091.2International Patent Application 119314.8125.WO00

[0113] for all k , l , n , m^^ . In other words, the information signal ^^ௗௗ^^^, ^^^ is quasi-periodic,with period M along the delay axis and N along the Doppler axis. The encoding of the MNinformation symbols to ^^ௗௗ^^^, ^^^ is carried out as in (4), so that ^^ௗௗ^^^, ^^^ is quasi-periodic, sinceonly quasi-periodic DD functions have TD realizations.

[0114] The information signal ^^ௗௗ^^^, ^^^ can then be converted to a continuous quasi-periodic DD^ ^ k^ M , l ^ N k , lsignal by lifting it to thedd ^ ^ p p ^ ^^ ^i.e.,

[0115] This signal^^^and ^^^alongthe delay and Doppler axes, respectively. That is, for all ^^, ^^ ∈ ℤ:

[0116] Note, in theused to denote a Dirac- delta function in a discrete domain and δ(^) is used to denote a Dirac-delta function in a continuous domain.

[0117] Pulse shape filtering in the DD domain can be implemented by twisted convolution. Twisted convolution of xdd(τ, ν) with a pulse shaping filter wtx(τ, ν) gives:

[0118] Since twisted, v ^is also quasi-periodic. Also, appropriate pulse shaping guarantees that the transmit TD Zak-OTFS modulated signal has time duration T and bandwidth B.

[0119] Note, in the present document, twisted convolution is denoted by ∗σ. Twisted convolution between two DD functions a(τ, ν) and b(τ, ν) can be given by: c^^, ^ ^^ a ^ ^ , ^ ^ ^^ b ^ ^ , ^ ^ ^^ ^ a ^ ^^ , ^ ^ ^ b ^ ^ ^ ^ ^ , ^ ^ ^ ^ ^ e j2^^^ ^ ^^ ^ ^ ^ d ^ ^ d ^ ^

[0120] b(τ, ν) ∗σ(c(τ, ν) ∗σd(τ, ν)) = (b(τ, ν) ∗σc(τ, ν)) ∗σd(τ, ν).

[0121] However, twisted convolution is not commutative, i.e., a(τ, ν) ∗σ b(τ, ν) ≠ b(τ, ν) ∗σ a(τ, ν). 182120091.2International Patent Application 119314.8125.WO00

[0122] The inverse Zak-transform of xw txdd ^^ , v ^gives a transmit TD Zak-OTFS modulated signal that is represented as:

[0123] Equivalently, theby:

[0124] Herein, ζk,l(t) is thesymbol x[k, l]. Previously referenced FIG. 11 provides an illustration of the Zak-OTFS carrier waveform. In the DD domain it is a quasi-periodic pulse. In both the TD / FD domains, the carrier waveform is a pulse train modulated by a tone and is therefore called a TD / FD pulse-tone.

[0125] In FIG. 11, the (k, l)-th quasi-periodic DD domain pulse located at ^^^^, ^^^^ ൌ൫^^^^^⁄ ^^ , ^^^^^⁄ ^^ ൯ and its TD / FD realizations referred to as TD / FD pulse-tone. The TD pulse-tone comprises a finite duration pulse train modulated by a TD tone. The FD pulse-tone comprises of a finite bandwidth pulse train modulated by a FD tone. The location of the pulses in the TD / FD pulse train and the frequency of the modulated TD / FD tone is determined by the location of the DD domain pulse (τ0, ν0). The time duration and bandwidth of a pulse-tone are inversely proportional to the characteristic width of the DD domain pulse along the Doppler axis and the delay axis, respectively. As τp→ ∞, the TD pulse-tone approaches a single TD pulse which is suited for delay-only channels. Similarly, as νp→ ∞, the FD pulse-tone approaches a single FD pulse which is suited for carrying information in Doppler-only channels. Zak-OTFS is therefore a family of modulations parameterized by τpthat interpolates between TD pulse modulation (TDM) and FD pulse modulation (FDM).

[0126] FIGS. 13 to 15 show three examples for different implementations of equations (1) and (2).

[0127] FIG. 13 shows a method of OTFS waveform generation in which the delta trains ∆^^,^^^^^^^are multiplied by the delay-Doppler grid elements ^^^^^, ^^^. The resulting signal isconvolved with ^^ఛ^^^^to obtain the output signal. Here, the signal is composed inthe delay domain. 182120091.2International Patent Application 119314.8125.WO00

[0128] FIG. 14 shows an embodiment in which the convolution operation is performed before adding the resulting signals together. In other words, signal is composed in the Doppler domain.

[0129] FIG. 15 shows the example where pulse-tone signals are multiplied by grid elements and the result is combined to obtain the transmission waveform.

[0130] Note that there may be other equivalent implementation of equations (1)-(3). For example, the time-domain signal can be rewritten as: ெି^ ேି^ ^ ^^^^^^ ^^ ^ ∙ ^ ^^^ଶగ^∆ఔ^ఛ

[0131] than the given examples in FIGS. 13-15.

[0132] 5.2 Examples implementations of the Zak transform

[0133] As discussed above, the definition of a DD domain pulse depends on a delay period ^^^,and a Doppler period ^^^, where the two periods are reciprocal, that is ^^^^^^ ൌ 1. The Zaktransform, denoted ^^௧, provides a unitary equivalence between TD signals and a subclass of quasi-periodic DD domain signals. The Zak transform of a TD signal x(t) is given by:

[0134] The quasi-.

[0135] Herein, it isaxis with period ^^^,and that it is quasi-periodic along with delay axis with period ^^^.

[0136] The inverse Zak transform, denoted by ^^௧ି^, of a quasi-periodic DD domain signal^^ௗௗ^^^, ^^^ is given by:

[0137] In some (TD) pulse-tones andcarrier waveforms for Zak-OTFS can be explained as follows. The transmit TD signal std(t) is given by 182120091.2International Patent Application 119314.8125.WO00 (5) where std,k,l (t) is the carrier, given by (6)

[0138] The FD(t) is given by (7) where(8) is the Fourier transformis (9) where, (10)is a quasi-182120091.2International Patent Application 119314.8125.WO00

[0139] From (9) and (10) it follows that the DD representation of the Zak-OTFS carrier waveform is given by (11) which is a quasi-period ^ 0 , is located at (kτp / M, lνp / N) (see FIG. 11 that represents a Zak-OTFS carrier waveform).

[0140] Carrier waveforms having unlimited time and bandwidth: For wtx(τ, ν) = δ(τ) δ(ν), it follows from (6) that . (12)

[0141] For (k, l) = (0, 0),(13) which is simply an infinitet=nτp. The (k, l)-th carrier waveform std,k,l(t) = xk,l(t) is nothing but std,0,0(t) with a Doppler shift of lνp / N and a delay shift of kτp / M, since it can be checked that . (14)

[0142] Note DDk^domain impulse at ^ pM , lv pN ^ (see right-hand side of (10)). The (k, l)-th carrier waveform, whichwe refer to as a TDis simply a train of impulses where the n-th impulse is located at j2 ^lvp ( t^ k ^τp+ kτp / M, modulated by a complex tone / sinusoidNpM )t=n e (see (6)).

[0143] It is clear from (8) that the FDl)-th TD pulse-tone is an FD e^j 2^fk^p Mimpulse train (with m-th impulse at f = mνp+ lνp / N) modulated by a FD tone . We refer to this waveform as a FD pulse-tone. When wtx(τ, ν) = δ(τ) δ(ν), it follows from (6) and (8) that the corresponding carrier waveforms have infinite time duration and bandwidth. 182120091.2International Patent Application 119314.8125.WO00

[0144] Carrier waveforms with limited time and bandwidth: The carrier waveforms can be limited in time duration and bandwidth by choosing an appropriate wtx(τ, ν). If the delay spread of wtx(τ, ν) is approximately 1 / B, and the Doppler spread is approximately 1 / T, then the TD pulse- tones have time duration T and bandwidth B. It follows from (6) that std,k,l (t) is simply xk,l (t) spread by 1 / B in the time domain. Given the structure of xk,l(t), it is clear that the TD pulse-tone std,k,l (t) consists of a train of narrow pulses modulated by a tone, with each narrow pulse having spread 1 / B and adjacent pulses separated by τp seconds. Similarly, from the integral expression in (7) it follows that the FD representation of the (k, l)-th carrier waveform, i.e., sfd,k,l(f), is simply Xk,l(f) spread by 1 / T in the frequency domain, since the Doppler domain spread of wtx(τ, ν) is 1 / T. Given the structure of Xk,l (f) in (8), it follows from the integral expression in (7) that the FD representation of the carrier waveform, i.e., sfd,k,l(f) consists of a train of narrow FD pulses modulated by a FD tone, with each narrow pulse having spread 1 / T and adjacent pulses separated by νp Hz. Therefore, std,k,l (t) also has a pulse-tone structure in the FD, and is referred to as a FD pulse-tone. FIG. 17 illustrates the TD and FD representations of the Zak-OTFS carrier waveform.

[0145] Time and Band-limited pulse-tones

[0146] For factorizable pulse shaping waveform wtx(τ, ν) = w1(τ) w2(ν), it follows from (6) that the (k, l)-th carrier waveform is given by (15) where(16) is the inverse Fourier transform. (17)

[0147] Then, x2,k,l(t) has in (15)we obtain 182120091.2International Patent Application 119314.8125.WO00 (18) where denotes the usual(19) where W1(f) and X2,k,l (f)by (20)

[0148] It is clearto thebandwidth of w1(∙). For example, choosing ^^^^^^^ ൌ √^^ ∙ sinc^^^^^^ limits the bandwidth of thecarrier waveforms to exactly B Hz. In general, for a given bandwidth constraint B, w1(τ) must have a spread of approximately 1 / B along the delay domain. Similarly, from (17) it follows that the duration of x2,k,l (t) can be limited to approximately T seconds by choosing the factor pulse w2(ν)to have a spread of approximately 1 / T along the Doppler domain (for example, with ^^ଶ^^^^ ൌ √^^ ∙sinc^^^^^^, x2,k,l (t) is limited exactly to the TD interval [−T / 2, T / 2]). Therefore, x2,k,l(t) = xk,l (t) W2(t) contains only T / τp= N number of Dirac-delta impulses of the infinite impulse train xk,l(t). Also, due to the TD convolution in (18), in the carrier waveform std,k,l(t) these N impulses are spread over a duration of approximately 1 / B seconds since the spread of w1(τ) is 1 / B. Therefore, under a finite duration and bandwidth constraint, the (k, l) carrier waveform consists of narrow pulses at t = nτp+ kτp / M where the width of each pulse is 1 / B = τp / M (since M = Bτp). Note that τp / M is also the time between the location of the n-th pulses of the (k, l)-th and the (k+ 1, l)-th carrier waveforms.

[0149] 6 Examples of OTFS Receivers

[0150] Different receivers may be used for receiving OTFS signals, wherein equalization may be performed in the delay-Doppler domain, when using OTFS with a set of predefined basis signals. For example, as described in the present document, the basis signals may combine certain mathematical properties of a pulse and a tone, and may be called Pulsones™. 182120091.2International Patent Application 119314.8125.WO00

[0151] Channel estimation may be performed by assigning to one or more delay-Doppler grid elements a known symbol (pilot) at the transmitter. At the receiver, the received signal may be processed for finding out the grid elements and their values where the pilot symbol was transformed to by the channel interaction. Furthermore, sensing signals, as described herein, may be used for performing channel sensing.

[0152] Let’s consider a pilot symbol that was assigned at the transmitter to the grid location ൫^^^,^^^൯, and received after the channel interaction at grid locations^^^^,^^^^with receivedvalues ℎ^, for ^^ ൌ 1,2, … ,Ω.

[0153] other than the pilot, a receiver will transform the estimated channel response obtained from the pilot to other locations on the grid, by rotating it: ℎ^ ^ଶగ∙^^^^^,^^^ ൌ ℎ^ ∙ ^^൫^,^,^^,^^,ே,ெ൯ (21)

[0154] Herein, ^^^∙^ is athegrid dimensions ^^ ൈ ^^.

[0155] 7 Example use cases for OTFS

[0156] An OTFS waveform generated as described herein may be used in a variety of different digital communication scenarios such as Under water acoustic wave communications, Deep- space communication, communication with non-terrestrial equipment such as satellites, airborne devices such as airplanes, balloons, drones, etc. The communication channel in such cases may comprise aerial-to-ground, ground-to-aerial or aerial-to-ariel communication, underwater acoustic wave communication deep space communication and so on. Furthermore, the disclosed techniques may be applied in generally any frequency range - from sub-MHz (e.g., underwater acoustics that uses 10 Hz to 1 MHz), MHz, GHz or THz and beyond. The OTFS waveform may occupy a pre-determined frequency and time domain widths.

[0157] 8 Example embodiments of sensing signal transmission / reception using OTFS

[0158] In some embodiments, OTFS transmitter may perform signal transmissions by tiling the OTFS frames onto respective tiles. Each time may comprise a data frame and / or a control channel or a pilot transmission. Various transmissions may be multiplexed using one or more of the different techniques described herein.

[0159] With respect to the numerology used in the two-dimensional resource plane, it may be possible to maintain numbers compatible with similarly structured orthogonal frequency division 182120091.2International Patent Application 119314.8125.WO00 multiplexing (OFDM) schemes that are used by current wireless standards such as LTE (long term evolution) and New Radio for the fifth generation (5G NR) standard. In particular grids corresponding to OFDM PRB grid (12 x 14) though aspect ratio permuted (e.g., 12 Doppler and 14 delay versus 14 symbols and 12 tones) may be used.

[0160] One example implementation may use 1 millisecond (ms) time units over available transmission bandwidth. This transmission resource unit may be divided into a 14x1272 dimension OTFS frame (as further disclosed below).

[0161] FIG. 16 shows examples of time slots used within the 1 ms time resource for each of the 14 OTFS frame, i.e., the top row showing the available OTFS frame, and the next three rows showing different allocations. In the example in the third row, the 1 ms time is split into 180 KHz frequency resource units, which makes up 106 OTFS frames in a 14×12 grid. In the example in the fourth row, the transmission resources split into 0.5 msec units, each having 360 KHz bandwidth, which also results in 106 OTFS frames in a 14×12 grid.

[0162] FIG. 17 shows examples of frame allocation based on the number of subcarriers and bandwidth, which affect complexity considerations, for different OTFS frame configurations. That is, complexity is reduced due to use of pulse-tone waveforms as sensing signals. For theM×N frame shown in FIG. 17, the complexity for an N-point FFT is ^^ ∙ log^^^^ and thecomplexity for M × N-point FFT is ^^ ∙ ^^ ∙ log^^^^. Similarly, for the N×M matrix show in FIG.17, the complexity for N × M-point FFT is ^^ ∙ ^^ ∙ log^^^^. In the example shown, M = 14 and N= 300 @ 5 MHz, 600 @ 10 MHz, 1200 @ 20 MHz.

[0163] Thus, in comparing the two scenarios in FIG. 17, the complexity ratio and the complexity savings are determined as shown below.plane in which each OTFS frame under scenarios of different carrier bandwidths. Data frames may be transmitted by organizing resource tiles into 1 msec time width and a corresponding 182120091.2International Patent Application 119314.8125.WO00 frequency bandwidth. Two examples, one with 720KHz bandwidth and another with 1440 KHz are shown.

[0165] FIG.19 shows an example of a time-frequency tiling of a physical resource block. In some examples, each PRB may correspond to 12 units in the delay dimension and 14 units in the Doppler dimension. As shown therein, PRBs are tiled along time / frequency dimensions such that each PRB corresponds to an OTFS frame that includes a first number of Doppler units (14) and a second number of delay units (12). The PRBs are organized along the frequency axis as having a first bandwidth (168 times (1+α) KHz) and along time axis as having a certain time duration (1 ms). The 12 delay units of PRB 5 are shown as an example illustration.

[0166] FIG.20 shows an expanded view of the delay-Doppler domain organization of transmission resources. The example shown in FIG.20 illustrates 14 frequency domain units, each representing 180 KHz, corresponding to 12 subcarriers spaced at 15 KHz.

[0167] FIG.21 shows another example of time frequency domain tiling of PRBs. Here, the units of time and frequency correspond to the embodiment depicted in the bottom row of Slide 2, with 0.5 msec time units and 336*(1+α) frequency units along the frequency axis.

[0168] FIG.22 shows another example of tiling along delay-Doppler axis. Here, the portion used in the time-frequency plane comprises 1 msec time, and an entire frequency bandwidth. The PRBs are depicted along the delay-Doppler two-dimensional plane as OTFS frames comprising 14 Doppler units and 12 delay units in each PRB.

[0169] FIG.23 shows an example arrangement along delay-Doppler two-dimensional plane in which eight PRBs are depicted, with a guard band (or inter-PRB spacing) being used in the delay domain (and across all Doppler).

[0170] FIG.24 shows examples of time-frequency tiles that can be allocated to various signals. In some embodiments, the area of each of the tile correlates to the amount of data that can be carried using the transmission resources represented by the tile. Different examples show assignments that are “square” in both time and frequency dimensions, or skinny-tall, meaning narrowband but using more time resources or wide-short, meaning higher bandwidth but less transmission time. It will be appreciated that because of the underlying OTFS modulation mechanism, the tiles can be individually demodulated at the receiving side. Thus, the OTFS 182120091.2International Patent Application 119314.8125.WO00 based tiling of PRB offers a design-trade off with respect to latency (smaller latency for tiles that occupy smaller time) and spectrum occupancy.

[0171] For example, often, in digital communication, a latency budget or a bandwidth budget is allocated to a particular data flow (or service). This prescribed bandwidth or latency budget may impact how transmission resources should be allocated for that particular transmission, and can be used to determine the area of the corresponding time-frequency tile for that particular data flow (or service).

[0172] FIG.25 shows an example of how OTFS-based transmission for multiple user devices or data channels or control channels can be organized. For simplicity, each time is shown as a rectangular region in time-frequency two-dimensional space, which includes an OTFS pulse having the specified bandwidth and the specified time duration. In this drawing, no guard bands are explicitly shown as separating the adjacent tiles.

[0173] The tiling example shown in FIG.25 also illustrates how tiles may be selected to have time- and frequency-domain measurements that are an integer multiple of a smallest unit. As shown therein, 0.125 msec is the smallest unit of time and 1 / 12thof the frequency band is the smallest unit of frequency. In some embodiments, data portion may be mapped to the 1 ms wide tile (rightmost four tiles in FIG.25), while control channels may be assigned to the different rectangular tile options on the left. Use of such a signal in digital communication may alleviate a need on the received device side to buffer large amounts of data by making control channel transmissions available in a relatively short time period. On the receiver side, and with knowledge of the tile dimensions, such samples can be recovered using a rectangular grid of received time-frequency samples (e.g., a train of pulses of a certain width and a certain bandwidth), converted into the OTFS domain, and underlying information recovered therefrom.

[0174] In some embodiments and / or implementations, the tiles may be separated from each other using guard bands (e.g., more generally, gaps; more specifically, inter-tile spacings, inter-frame spacings, inter-PRB spacings) to take into account finite roll-offs of filters in typical software or hardware implementations.

[0175] FIG.26 shows an example of how sensing signals may be multiplexed into time- frequency tiles that carry data or control signals. Here, each tile may represent a data frame that is either punctured or separated by a gap, guard band, or inter-frame spacing. The exact time- or 182120091.2International Patent Application 119314.8125.WO00 frequency-domain size of these gaps may be determined based on operational considerations, as is described in the present document. As further described in the present documents, pulse-tone signals, used as pilots or reference signals for sensing, may be inserted in these gaps based on operational scenarios and physical layer parameters. Looking along the time axis at gaps in the set of frames with same frequency width along the frequency width, it can be seen that the period with which the sensing signals are placed within the 2D resource plane varies, with more often in the frames in Region A, less often in Region B, and least often in the rightmost data frames in Region C. Put differently, the pulse train of the sensing signal for each of these data frame patterns has a different time periodicity.

[0176] In these examples, the longer sensing signal periodicity may be used to get a better Doppler resolution in channel sensing (e.g., based on the duality principle). For example, a channel with a relatively low motion or static channel may be sampled less often, which means that the sensing signals may use less periodicity along the time axis, compared to channel with a faster moving user device. For such a channel, Doppler spread may be relatively small. In one example embodiment, each data frame in the drawing may represent an uplink transmission, with the data frames collectively representing uplink data transmissions from multiple user devices. The gaps may be allocated for sensing either the same user device that is making uplink transmission adjacent to the gap, or could be allocated for a different user device. For example, the gaps among data frames in Region A be used by wireless device 1, the gaps in the data frames in Region B may be used by wireless device 2m and the gaps in the data frames in Region C may be used by wireless device 3.

[0177] FIG.27 shows additional details of how sensing signals may be positioned within the time-frequency 2D resource plane with different periodicities. Here, three different sensing signals (SS) are shown: SS1, SS2 and SS3 in a scenario where data frames have 1 msec width and span the entire frequency of interest. As can be seen, different SS can be sent with different periodicities, generally based on an expected channel behavior such as Doppler spread. Here, SS3 is being sent least often, meaning that the channel may be the most static channel (e.g., a non-moving or slow-moving user), while SS2 is being sent most often, representing a channel whose Doppler spread may be large (e.g., a fast-moving user). 182120091.2International Patent Application 119314.8125.WO00

[0178] FIG.28 shows another example of an arrangement of sensing signals in a 2D time- frequency resource plane. Here, it can be seen that different sensing signals may have different periodicities and occupy different frequency bandwidths. The time-frequency parameters (e.g., repetition rate in time domain and bandwidth in frequency domain) may be a function of an expected delay and Doppler behavior of the channel being targeted for sensing by the signal. Here, the left-most data frames show a sensing signal with 1 msec periodicity and one unit frequency width, while the left portion shows four different types of sensing signals, some that have one unit of frequency bandwidth and 2 msec periodicity and others that have half unit frequency bandwidth and 2 or 4 msec periodicity.

[0179] FIG.29 shows a numerical example of sensing signals in the 2D resource plane. Here, the time-frequency frame shown is similar to frames currently being used in OFDM systems with 15 kHz subcarrier spacing and 1 msec time domain width, which is split into 15 units of 66.67 microseconds each. The frequency bandwidth (5.76 MHz) is split into 8 × 4 × 12 × 15 kHz units. Therefore, the parameters N and M may be N = 14 and M = 48 (4×12). As shown by a representative example in the top row, 14 intervals are used for a pulse train carrying data frames. The depicted example may have 12 carriers that are 15 kHz apart, and 4 PRBs per row, resulting in 720 kHz per unit of vertical framing. In FIG.29, the left-top resource element represents the gap that can be allocated to SS. Here, SS may be introduced as pulse-tones having their own pre-selected time and frequency spreads, such as 1.39 microsecond time and 1 KHz frequency spread. Although the SS are shown to occupy a single cell in this figure, they could also be designed to have a greater bandwidth along frequency domain (e.g., could be taller lines).

[0180] FIG.30 shows another example of sensing signals within a 2D resource plane. This example shows a zoomed in version of the sensing signals illustrated in FIG.29. As shown in FIG.30, the SS are placed in a 66.67 microsecond time interval corresponding to a gap (or inter- frame spacing). Each pulse has a bandwidth of 1 / 720KHz, which is approximately 1.39 microseconds. It will be seen that there is room to accommodate as many as 25 such SS, which are multiplied in frequency. Each pulse-tone may be sent every ^^^= 4.7 microsecond to sense a different channel (to take into account delay spread at the receive time). Each pulse-tone in the center portion of FIG.30 (visually represented as a grating of horizontal lines) may represent SS for one channel for one user device, giving about 14 user device SS capability. Leveraging the 182120091.2International Patent Application 119314.8125.WO00 opportunity to multiplex 25 such signals in the frequency domain, and by taking into account Doppler spread, it may be possible to send 2 such signals of half the full length. Therefore, the depicted arrangement may allow up to 700 different channels to be sensed using the transmission resource mapping. It will be appreciated that the specific numbers in this example are not critical, but show that this scheme entails accommodating a large number of user devices for channel sensing using realistic operational parameters (i.e., Doppler and delay estimates). It will further be appreciated that sensing a channel in one direction (e.g., uplink) can be used to estimate a corresponding downlink channel (and vice versa) also. This technique may especially be used in a massive multi-input multi-output (MIMO) system where there are many channels present corresponding to different combination of transmit and receive antennas. In addition, precoding may be used to further increase number of channels that can be sensed by providing directionality to the transmission of SS signals.

[0181] FIG.31 shows an example of multiplexing signals along a 2D resource plane. Here, an example of tiles used for data frame transmissions are depicted along with an example of sensing signals being inserted in gaps that occur every 5thframe. In other words, the periodicity of SS is Tp = 5 time units (5 msec in this example).

[0182] FIG.32 illustrates additional details associated with the insertion of sensing signals in gaps, according to one particular implementation example. In FIG.32, the top horizontal axis shows the insertion of pulse-tone sensing signals arranged along the Doppler axis with a periodicity of ^^^, to sense k number of wireless devices (e.g., UEs). Herein, Doppler shaping filters and / or windowing can be used to avoid spilling over across users. As show in the rectangular inset in FIG.32, the resulting signal, in the delay-Doppler plane, will have a number of pulses (N representing number of pulses, and M representing how many pulses can be fit within the bandwidth). Thus, N will be equal to the frame period ^^ி, divided by pulse periodicity ^^^, while M will be equal to pulse bandwidth BW multiplied by ^^^.

[0183] FIG.33 is an example of a signal transmission arrangement based on a number of parameters in a specific relationship that influences the selection of frame size, gap size, etc. to determining a number of pulse-tone signals that can be used for channel sensing. In an example implementation, the following constraint is implemented: ^^^1 #PRB / 4 ൈ ^^ி / ^^ௌ ൈ ൬^^^ ൈ ൬^^^ Ω ^^ ^ 5000.182120091.2International Patent Application 119314.8125.WO00

[0184] In the above formula, ^^ிis the frame time, ^^ௌis the channel sensing repetition time, ^^^is the gap size, ^^ௌis the expected delay spread, and Ωௌis the expected Doppler spread. In this example, over 5000 user channels could be senseda quarter of a second using the following parameter values: ^^^ ൌ 66.67 ^^^^ ^^ி ൌ 1 msec ^^ௌ ൌ 5 msec Ωௌ ൌ 40 Hz[0018users 1 to 4). In this example, the frame time ^^ிis equal to 250 msec and SS periodicity is equal to 5 msec. Therefore, in the frame time of 250 msec, each user’s ±25 Hz Doppler may be accommodated by multiplexing 200 Hz because the frame time offers a resolution of 4 Hz sampling rate. As shown in FIG.34, each user device’s SS may be sent in a non-overlapping manner. Here, the pulse-tone pilots offer the opportunity to interleave both in the doppler and the time domains. This can be achieved by overlapping pulse trains for each SS with appropriate rotations that orthogonalizes it with respect to the other SS.

[0186] FIG.35 illustrates the concept of pulse-tone signal multiplexing for multiple users. As shown therein, the bottom graph shows a resolution used to sense the channel. The finer Doppler resolution needed for sensing the channel can be achieved by extending the SS pulse trains over a longer time. The middle graph shows a bank of filters that captures or represents the effective data channel that may be experienced by a data frame. The top graph shows an example of the actual (true) channel characteristic (e.g., Doppler spread). In this example, the SS may be applied over half a second (or 250 msec), while the channel experienced by data is over a 1 millisecond time interval. Put another way, the sensing signal may be used to rate upsample channel characteristics of a channel experienced by data.

[0187] FIG.36 shows an example of signal processing for oversampling the channel for sensing. From top to bottom , a channel is split into multiple smaller portions that represent the Doppler values experienced by certain signals, which then are further sampled or sensed using sensing signals of finer resolution (as described above in the context of FIG.35).

[0188] FIG.37 provides another example that further explains the idea of channel sensing using pulse-tone pulse trains. Here, the time frequency grid is shown over a 32 PRB and 1 msec interval. As shown in the top row, a data frame may occupy 14 units, with one (leftmost) gap 182120091.2International Patent Application 119314.8125.WO00 made available for SS transmissions. In this example, the SS occupies a gap at a leading time (i.e., prior to the upcoming data frame transmission). By sensing channel at this time, an expected channel response may be predicted for the upcoming data transmission.

[0189] FIG. 38 is another arrangement of frames and tiles in the 2D resource plane with 60 KHz subcarrier spacing (compared to 30 KHz in the example shown in FIG. 37), and a similar exposition is omitted. This example may be useful for accommodating the possibility of a greater Doppler spread.

[0190] FIG. 39 shows yet another resource plane arrangement in which 120 kHz subcarrier spacing is used (and again, for which, details are omitted). It is noted, however, that the repetition parameter values here are different from the previous examples.

[0191] FIG. 40 shows an example of the relationship between PRBs and subbands, in which the PRB allocation can be configured to span multiple subbands and / or fractions thereof. The depicted numerology comprises numbers similar to the existing fifth generation (5G) or long term evolution (LTE) systems. Here, four PRBs comprise one resource unit, corresponding to one Zak frame for the OTFS signals, with fourteen such units allocated to data frame and one unit allocated to a gap (or inter-PRB spacing) for sensing signals.

[0192] FIG. 41 shows a timing relationship between pulse-tone signals and sensing windows. In this particular example, a 20 MHz communication channel is used for the physical layer parameters enumerated below. ^^^ ൌ 66.67 ^^^^ ^^ௌ ൌ 1 msec ^^^ ൌ 1.39 ^^sz

[0193] Herein, ^^^ignal (e.g., Pulsone)repetition interval, ^^^is the width of the Pulsone, and ^^ௌand νௌare the delay spread and Doppler spread, respectively. The number of sensing signals (or pilots), denoted ^^ௌ, that can be configured for this type of system is determined as:

[0194] For the above parameterof a maximum delay spread of 4.7 microseconds and a maximum Doppler spread of ± 250 Hz, over 700 separate channels may be sensed using sensing signal transmissions in gaps. In another example, if only the bandwidth 182120091.2International Patent Application 119314.8125.WO00 (BW) of the system was changed to 18 MHz (instead of 20 MHz), then over 600 channels could be simultaneously sensed under the above assumptions.

[0195] FIG.42 shows an example arrangement of sensing signal transmissions based on delay spread. Here, low-latency signals are included in an initial portion, wherein the resource tiles look “skinny tall” due to narrow time and full bandwidth assignment (with corresponding sensing signals taking on similar properties), mid-latency signals comprise half-bandwidth, double-time tiles, with corresponding sensing signals having a similar structure of longer time separation (periodicity), and high-latency signals having less bandwidth but a greater time allocation. It will be appreciated that the low-latency signals also constitute low delay spread signals, medium-latency signals correspond to medium delay spread signals, and so on. Therefore, the corresponding arrangement of sensing signals advantageously matches the delay spread characteristics of the channel being sensed.

[0196] FIG.43 shows an example of an OTFS waveform. The waveform shows a delay-Doppler domain pulse that has been filtered and converted into a time-domain train of pulses, where each pulse (pulse-tone) has a phase shift that varies (middle portion of the drawing) such that the resulting waveform is invariant under time, delay or Doppler domain shifts. As discussed in this patent document, the invariance of the resulting waveform to time, delay or Doppler domain shifts can be achieved by configuring each pulse of the train of pulses with a delay period and a Doppler period that are greater than an expected (or maximum) delay spread and an expected (or maximum) Doppler spread, respectively.

[0197] FIG.44 shows a digital communication processing example in which each Zak transform unit comprising four PRBs in the delay-doppler domain is processed through a Zak transformed, followed by a channelizer (which may be an inverse fast Fourier transform or a filter bank multi- carrier (FBMC)) processing stage, which results in a time-domain signal.

[0198] FIG.45 shows sensing signal examples and how periodicities can be scaled depending on numerology of the resource plane. As shown therein, the same number of users can be supported and / or sensing signals can be used for different system parameters.

[0199] FIG.46 shows an example of a resource plane in which the one or more gaps are allocated for transmission of sensing signals. As shown therein, the inter-resource (e.g., with the resources being frames, tiles, PRBs, etc.) gaps or spacings for the transmission of sensing signals 182120091.2International Patent Application 119314.8125.WO00 can be allocated across the entire bandwidth, and periodically spaced to span the entire 1 msec duration of the resource.

[0200] 9 Examples of co-existence with other channel estimation tools

[0201] It will be appreciated by those of skill in the art that channel delay spreads cause data signals to spill into sensing portion of the resources. This interference may occur on a long term sensing signal periodicity. To mitigate any corruption of sensing procedure, an overlay of short term channel estimation, such as performed using demodulation reference signals (DMRS) may be overlaid with results obtained from long-term channel sensing performed using OTFS sensing signals. In some embodiments, different orthogonalization codes may be used for the short term and long term frames used for sensing in a cell, with codes used by different cells being orthogonal to each other.

[0202] 10 Examples of power profiles and other operational considerations

[0203] In some embodiments, a power profile of a receiving device at the receiving end of a channel may be taken into consideration when selecting the periodicity and placement of sensing signals within gaps interspersed with data frames. For example, a low power device, which should be in a mode in which its receiver is turned off most of the time, may be targeted with low periodicity such as 5 to 10 milliseconds. Examples of such devices include small, battery operated devices such as internet of things (IoT) devices. Advantageously, such devices are often in a static situation where there is none or very little relative movement between the device and a transmitter at a base station. Therefore, Doppler spread for such channels will be relatively small, and therefore spacing out sensing channel transmissions with a greater distance may work fine in such cases without degradation of performance. Conversely, devices that are fast moving often tend to have a greater battery budget, a higher Doppler spread, and therefore sensing signals may be scheduled more often. In another aspect, for low power profile devices, their corresponding sensing signals and data frames may be scheduled to occur contiguously in time. Thus, the receiver can wake up, receive both the signals and then go back in sleep mode, without having to wake up again just to receive only one signal type (data, pilot or sensing signals).

[0204] 11 Example embodiments of the disclosed technology

[0205] FIG.47 is a flowchart of a method 4700 of digital communication. The method 4700 includes performing (4710), for multiple users, a plurality of channel sensing signal 182120091.2International Patent Application 119314.8125.WO00 transmissions using transmission resources in a plurality of inter-tile spacings separating resource tiles in a two-dimensional resource plane, and receiving (4720), for each of at least two users of the multiple users, one or more parameters associated with a resource tile allocated to a corresponding user. In this example method, the plurality of channel sensing signal transmissions comprises signal waveforms determined using basis functions that are invariant under operations of time, delay, and Doppler shift.

[0206] FIG.48 is a flowchart of a method 4800 of digital communication. The method 4800 includes receiving (4810), multiple users, a plurality of channel sensing signal transmissions on transmission resources in a plurality of inter-tile spacings separating resource tiles in a two- dimensional resource plane. The method further includes determining (4820), based on the plurality of channel sensing signal transmissions, one or more parameters associated with a resource tile allocated to each of at least two users of the multiple users, and transmitting (4830) the one or more parameters corresponding to the at least two users. In this example method, the plurality of channel sensing signal transmissions comprises signal waveforms determined using basis functions that are invariant under operations of time, delay, and Doppler shift.

[0207] The following solutions may be preferably implemented by some embodiments.

[0208] P1. A method of digital communication, comprising: performing one or more channel sensing signal transmissions using transmission resources in one or more gaps separating resource tiles in a two-dimensional resource plane; and sensing one or more channels using the one or more sensing signal transmissions, wherein the one or more channel sensing signal transmissions comprise signal waveforms that use basis functions that are invariant under operations of time, delay and Doppler shifts.

[0209] P2. A method of digital communication, comprising: receiving one or more channel sensing signal transmissions on transmission resources in one or more gaps separating resource tiles in two-dimensional resource plane; and facilitating a channel sensing operation based on reception of the one or more sensing signal transmissions, wherein the one or more channel sensing signal transmissions comprise signal waveforms that use basis functions that are invariant under operations of time, delay and Doppler shifts.

[0210] P3. The method of solution P1 or P2, wherein each signal waveform comprises a train of pulse-tone pulses defined by a time width in time domain and a bandwidth in frequency domain. 182120091.2International Patent Application 119314.8125.WO00

[0211] P4. The method of solution P3, wherein each signal waveform is orthogonal with respect to remaining signal waveforms at least in a time domain, a frequency domain, a delay domain, a doppler domain or a spatial direction domain.

[0212] P5. The method of solution P3 or P4, wherein an ith train of pulse-tone pulses has a periodicity TP(i), wherein i is an integer variable and wherein the periodicity is inversely proportional to an expected doppler shift of a channel being sensed by a channel sensing signal transmission that comprises the ith train of pulse-tone pulses.

[0213] P6. The method of solution P1, wherein the resource tiles in the two-dimensional resource plane are organized as frames that repeat in the two-dimensional planes, where each frame is defined by a frame duration and a frame bandwidth.

[0214] P7. The method of solution P6, wherein a number of channel sensing signal transmissions included in each of the one or more gaps, a periodicity of repetition of channel sensing signal transmission for a particular channel, a frequency bandwidth of a channel sensing signal transmission for the particular channel, and / or a total number of channels for which channel sensing signal transmissions are included within a single frame in the two-dimensional resource plane are determined according to an expected maximum delay spread and / or an expected maximum doppler spread of channels for which the channel sensing signal transmissions in the single frame are performed.

[0215] P8. The method of any of solutions P1 to P7, wherein a periodicity of a particular channel sensing signal transmission depends on a power profile associated with a corresponding channel over which the particular channel sensing signal transmission is performed.

[0216] P9. The method of solution P1, wherein the two-dimensional resource plane comprises a time-frequency plane wherein transmission resources are organized according to an expected delay spread and / or an expected doppler spread of channels over which transmissions are performed, and wherein each resource tile is configured to carry orthogonal time frequency space signals (OTFS) comprising pulse-tone waveforms.

[0217] P10. The method of solution P1, wherein a particular channel sensing signal transmission that is performed in a particular gap is performed on a channel on which a data frame in a resource tile adjacent to the particular channel is transmitted. 182120091.2International Patent Application 119314.8125.WO00

[0218] P11. The method of solution P1, wherein a particular channel sensing signal transmission that is performed in a particular gap is performed on a different channel than another channel on which a data frame in a resource tile adjacent to the particular channel is transmitted.

[0219] P12. The method of any of solutions P1 to P11, wherein the basis functions are time realizations of a filtered quasi-periodic delay-doppler domain delta.

[0220] P13. The method of any of solutions P1 to P12, wherein the signal waveforms are generated using a Zak transformation.

[0221] P14. The method of any of solutions P1 to P13, wherein the signal waveforms are generated using a filter bank.

[0222] P15. The method of any of solutions P1 to P14, wherein the one or more channel sensing signal transmissions are assigned to the one or more gaps based on a latency budget for a corresponding channel that is being sensed.

[0223] P16. The method of solutions P1 and P3 to P15, wherein the sensing the channel comprises receiving a response signal that is generated in response to a corresponding channel sensing signal transmission.

[0224] P17. The method of any of solutions P2 to P15, wherein the facilitating the channel sensing operation comprises: receiving a channel sensing signal transmission corresponding to a particular channel and providing a response signal that provides one or more parameters that are based on the receiving the channel sensing signal transmission.

[0225] P18. A digital communication apparatus comprising at least one processor, wherein the at least one processor is configured to cause the digital communication apparatus to implement a method recited in any one or more of solutions P1 to P17.

[0226] P19. A computer-readable medium having code stored thereon, the code, upon execution by at least one processor, causing the at least one processor to control a digital communication apparatus to perform a method recited in any one or more of solutions P1 to P17.

[0227] The following solutions may preferably be used by some embodiments.

[0228] N1. A method of digital communication, comprising: performing, for multiple users, a plurality of channel sensing signal transmissions using transmission resources in a plurality of inter-tile spacings separating resource tiles in a two-dimensional resource plane; and receiving, for each of at least two users of the multiple users, one or more parameters associated with a 182120091.2International Patent Application 119314.8125.WO00 resource tile allocated to a corresponding user, wherein the plurality of channel sensing signal transmissions comprises signal waveforms determined using basis functions that are invariant under operations of time, delay, and Doppler shift.

[0229] N2. A method of digital communication, comprising: receiving, multiple users, a plurality of channel sensing signal transmissions on transmission resources in a plurality of inter- tile spacings separating resource tiles in a two-dimensional resource plane; determining, based on the plurality of channel sensing signal transmissions, one or more parameters associated with a resource tile allocated to each of at least two users of the multiple users; and transmitting the one or more parameters corresponding to the at least two users, wherein the plurality of channel sensing signal transmissions comprises signal waveforms determined using basis functions that are invariant under operations of time, delay, and Doppler shift.

[0230] In these solutions, channel sensing may refer to the operation of determining channel parameters for a sparse representation of the channel, and which is performed less frequently than channel estimation using channel state information (CSI) or demodulation (DM) reference signals (RS).

[0231] In these solutions, a first coordination node (e.g., a base station in 5G or LTE systems) is configured to perform solution N1 and a second coordination node is configured to perform solution N2. Herein, the first and second coordination nodes are configured to support (e.g., provide connectivity to) multiple users (or user devices, e.g., UEs in 5G or LTE systems).

[0232] N3. The method of solution N1 or N2, wherein the one or more parameters comprises an expected maximum delay spread or an expected maximum Doppler spread of a channel over which a corresponding channel sensing signal transmission is performed.

[0233] N4. The method of solution N3, wherein each of the signal waveforms comprises a train of pulse-tone pulses defined by a time width in a time domain and a bandwidth in a frequency domain.

[0234] N5. The method of solution N4, wherein each signal waveform is orthogonal with respect to remaining signal waveforms at least one of the time domain, the frequency domain, a delay domain, a Doppler domain, or a spatial direction domain.

[0235] N6. The method of solution N4 or N5, wherein an ith train of pulse-tone pulses has a periodicity TP(i), wherein i is an integer, and wherein the periodicity is inversely proportional to 182120091.2International Patent Application 119314.8125.WO00 an expected Doppler shift of the channel being sensed by the corresponding channel sensing signal transmission that comprises the ith train of pulse-tone pulses. In these solutions, and as discussed in the context of FIGS.27 and 28, the periodicities of individual pulse trains may be selected according to an expected Doppler shift. For example, the relationship is inversely proportional, meaning that, for greater doppler shifts, smaller periods, i.e., more repetitions, may be used.

[0236] N7. The method of solution N3, wherein the resource tiles in the two-dimensional resource plane are organized as frames that repeat in the two-dimensional resource plane, and where each frame is defined by a frame duration and a frame bandwidth.

[0237] In any of these solutions, the resource tiles in the two-dimensional resource plane can be organized as frames (or tiles) that repeat in the two-dimensional planes, with each frame being defined by a frame duration and a frame bandwidth. Although various drawings show a single frame in the resource plane, it will be appreciated that the resource allocation may be repetitive, with details of repetitions omitted from the drawings for sake of visual clarity.

[0238] N8. The method of solution N7, wherein at least one of a number of the plurality of channel sensing signal transmissions included in each of the plurality of inter-tile spacings, a repetition period of the plurality of channel sensing signal transmissions for a particular channel, a frequency bandwidth of the plurality of channel sensing signal transmissions for the particular channel, or a total number of channels for which the plurality of channel sensing signal transmissions are included within a single frame in the two-dimensional resource plane is determined based on the expected maximum delay spread or the expected maximum Doppler spread of channels for which the plurality of channel sensing signal transmissions in the single frame are performed.

[0239] N9. The method of solution N7, wherein a number of the plurality of channel sensing signal transmissions included in an inter-tile spacing is based on the frame duration, a repetition period of the plurality of channel sensing signal transmissions, a time duration of the inter-tile spacing, an expected delay spread, and an expected Doppler spread.

[0240] N10. The method of solution N3, wherein a repetition period of a particular channel sensing signal transmission depends on a power profile associated with a corresponding channel over which the particular channel sensing signal transmission is performed for a particular user. 182120091.2International Patent Application 119314.8125.WO00

[0241] N11. The method of solution N10, wherein the repetition period is less than a first threshold upon determining that a velocity of the particular user is less than a second threshold.

[0242] N12. The method of solution N10, wherein the repetition period is equal to zero and the particular channel sensing signal transmission is performed continuously over a predefined duration upon determining that the power profile is indicative of a low power mode.

[0243] N13. The method of solution N10, wherein the repetition period is greater than a first threshold upon determining that a velocity of the particular user is greater than a second threshold.

[0244] N14. The method of solution N3, wherein the two-dimensional resource plane comprises a time-frequency plane wherein the transmission resources are organized according to an expected delay spread or an expected Doppler spread of channels over which transmissions are performed, and wherein each resource tile is configured to carry orthogonal time frequency space (OTFS) signals comprising pulse-tone waveforms.

[0245] N15. The method of any of solutions N1 to N3, wherein a particular channel sensing signal transmission that is performed in a particular inter-tile spacing is performed on a particular channel on which a data frame in a resource tile adjacent to the particular channel is transmitted.

[0246] N16. The method of any of solutions N1 to N3, wherein a particular channel sensing signal transmission that is performed in a particular inter-tile spacing is performed on a different channel than a particular channel on which a data frame in a resource tile adjacent to the particular channel is transmitted.

[0247] With regard to solutions N15 and N16, it is noted that the disclosed techniques advantageously enable the mixing of any data transmissions with any other channel sensing signals. However, from a power saving perspective, often, the channel sensing transmissions targeting a particular receiver (i.e., for a particular channel) may be sent adjacent to data frames being transmitted on that channel (to the particular receiver). One reason for this may be to manage reception operation of the receiver device such that the device only needs to wake up once to receive both the data frame and the channel sensing signals.

[0248] N17. The method of any of solutions N3 to N16, wherein each of the basis functions is determined based on time-domain realizations of a filtered quasi-periodic delay-Doppler domain delta function defined by a delay period and a Doppler period. 182120091.2International Patent Application 119314.8125.WO00

[0249] N18. The method of any of solutions N3 to N16, wherein each of the basis functions is determined based on a lattice in a delay-Doppler domain, defined by a delay period (τ_p) and a Doppler period (ν_p), which consists of a single quasi-periodic localized pulse in a region of the delay-Doppler domain defined by 0≤τ≤τ_p and 0≤ν≤ν_p.

[0250] N19. The method of solution N17 or N18, wherein the delay period is greater than or equal to the expected maximum delay spread and the Doppler period is greater than or equal to the expected maximum Doppler spread.

[0251] N20. The method of any of solutions N1 to N19, wherein the signal waveforms are generated using a Zak transformation.

[0252] N21. The method of any of solutions N1 to N19, wherein the signal waveforms are generated using a filter bank.

[0253] N22. The method of any of solutions N3 to N21, wherein the plurality of channel sensing signal transmissions are assigned to the plurality of inter-tile spacings based on a latency budget for a corresponding channel that is being sensed.

[0254] N23. The method of solution N22, wherein the expected maximum delay spread and the expected maximum Doppler spread are configured in proportion to the latency budget.

[0255] N24. The method of any of solutions N3 to N23, wherein a user of the at least two users of the multiple users is configured to: receive the one or more parameters associated with the resource tile allocated to the user; configure, using the one or more parameters, a transceiver of the first user; and using the transceiver to perform a transmission or a reception in the resource tile.

[0256] N25. The method of solution N24, wherein the transmission or the reception uses one or more data frames, and wherein configuring the transceiver comprises: configuring duration and bandwidth parameters of each of the one or more data frames based on the expected maximum delay spread or the expected maximum Doppler spread.

[0257] N26. A digital communication apparatus comprising at least one processor, wherein the at least one processor is configured to cause the digital communication apparatus to implement the method of any of solutions N1 to N25. 182120091.2International Patent Application 119314.8125.WO00

[0258] N27. A computer-readable medium having code stored thereon, the code, upon execution by at least one processor, causing the at least one processor to control a digital communication apparatus to perform the method recited in any of solutions N1 to N25.

[0259] FIG.49 is a block diagram representation of a wireless hardware platform 4900 which may be used to implement the various methods described in the present document. The hardware platform 4900 may be incorporated within a base station or a user device (e.g., a wireless device). The hardware platform 4900 includes processor electronics including one (or more) processor(s) 4902, one or more memories 4904 (this may be optional and in some cases the memory may be internal to the processor) and a transceiver circuitry 4906. The processor may execute instructions, e. g., by reading from the memory 4904, and control the operation of the transceiver circuitry 4906 and the hardware platform 4900 to perform the methods described herein. In some embodiments, the memory 4904 and / or the transceiver circuitry 4906 may be partially or completely contained within the processor 4902 (e.g., same semiconductor package).

[0260] 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. A propagated signal is an artificially generated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal, which is generated to encode information for transmission to suitable receiver apparatus. 182120091.2International Patent Application 119314.8125.WO00

[0261] A computer program (also known as a program, software, software application, script, or code) can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a standalone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program does not necessarily correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network.

[0262] The processes and logic flows described in this document can be performed by one or more programmable processors executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit).

[0263] Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read -only memory or a random access memory or both. The essential elements of a computer are a processor for performing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks. However, a computer need not have such devices. Computer readable media suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and 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. 182120091.2International Patent Application 119314.8125.WO00

[0264] While this patent document contains many specifics, these should not be construed as limitations on the scope of an invention that is claimed or of what may be claimed, but rather as descriptions of features specific to particular embodiments. Certain features that are described in this document in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable sub- combination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a sub-combination or a variation of a sub-combination. Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results.

[0265] Only a few examples and implementations are disclosed. Variations, modifications, and enhancements to the described examples and implementations and other implementations can be made based on what is disclosed. 182120091.2

Claims

International Patent Application 119314.8125.WO00 WHAT IS CLAIMED IS:

1. A method of digital communication, comprising: performing, for multiple users, a plurality of channel sensing signal transmissions using transmission resources in a plurality of inter-tile spacings separating resource tiles in a two- dimensional resource plane; and receiving, for each of at least two users of the multiple users, one or more parameters associated with a resource tile allocated to a corresponding user, wherein the plurality of channel sensing signal transmissions comprises signal waveforms determined using basis functions that are invariant under operations of time, delay, and Doppler shift.

2. A method of digital communication, comprising: receiving, multiple users, a plurality of channel sensing signal transmissions on transmission resources in a plurality of inter-tile spacings separating resource tiles in a two- dimensional resource plane; determining, based on the plurality of channel sensing signal transmissions, one or more parameters associated with a resource tile allocated to each of at least two users of the multiple users; and transmitting the one or more parameters corresponding to the at least two users, wherein the plurality of channel sensing signal transmissions comprises signal waveforms determined using basis functions that are invariant under operations of time, delay, and Doppler shift.

3. The method of claim 1 or 2, wherein the one or more parameters comprises an expected maximum delay spread or an expected maximum Doppler spread of a channel over which a corresponding channel sensing signal transmission is performed.

4. The method of claim 3, wherein each of the signal waveforms comprises a train of pulse- tone pulses defined by a time width in a time domain and a bandwidth in a frequency domain.

5. The method of claim 4, wherein each signal waveform is orthogonal with respect to remaining signal waveforms at least one of the time domain, the frequency domain, a delay 182120091.2International Patent Application 119314.8125.WO00 domain, a Doppler domain, or a spatial direction domain.

6. The method of claim 4 or 5, wherein an ithtrain of pulse-tone pulses has a periodicity TP(i), wherein i is an integer, and wherein the periodicity is inversely proportional to an expected Doppler shift of the channel being sensed by the corresponding channel sensing signal transmission that comprises the ithtrain of pulse-tone pulses.

7. The method of claim 3, wherein the resource tiles in the two-dimensional resource plane are organized as frames that repeat in the two-dimensional resource plane, and where each frame is defined by a frame duration and a frame bandwidth.

8. The method of claim 7, wherein at least one of a number of the plurality of channel sensing signal transmissions included in each of the plurality of inter-tile spacings, a repetition period of the plurality of channel sensing signal transmissions for a particular channel, a frequency bandwidth of the plurality of channel sensing signal transmissions for the particular channel, or a total number of channels for which the plurality of channel sensing signal transmissions are included within a single frame in the two-dimensional resource plane is determined based on the expected maximum delay spread or the expected maximum Doppler spread of channels for which the plurality of channel sensing signal transmissions in the single frame are performed.

9. The method of claim 7, wherein a number of the plurality of channel sensing signal transmissions included in an inter-tile spacing is based on the frame duration, a repetition period of the plurality of channel sensing signal transmissions, a time duration of the inter-tile spacing, an expected delay spread, and an expected Doppler spread.

10. The method of claim 3, wherein a repetition period of a particular channel sensing signal transmission depends on a power profile associated with a corresponding channel over which the particular channel sensing signal transmission is performed for a particular user.

11. The method of claim 10, wherein the repetition period is less than a first threshold upon determining that a velocity of the particular user is less than a second threshold. 182120091.2International Patent Application 119314.8125.WO00 12. The method of claim 10, wherein the repetition period is equal to zero and the particular channel sensing signal transmission is performed continuously over a predefined duration upon determining that the power profile is indicative of a low power mode.

13. The method of claim 10, wherein the repetition period is greater than a first threshold upon determining that a velocity of the particular user is greater than a second threshold.

14. The method of claim 3, wherein the two-dimensional resource plane comprises a time- frequency plane wherein the transmission resources are organized according to an expected delay spread or an expected Doppler spread of channels over which transmissions are performed, and wherein each resource tile is configured to carry orthogonal time frequency space (OTFS) signals comprising pulse-tone waveforms.

15. The method of any of claims 1 to 3, wherein a particular channel sensing signal transmission that is performed in a particular inter-tile spacing is performed on a particular channel on which a data frame in a resource tile adjacent to the particular channel is transmitted.

16. The method of any of claims 1 to 3, wherein a particular channel sensing signal transmission that is performed in a particular inter-tile spacing is performed on a different channel than a particular channel on which a data frame in a resource tile adjacent to the particular channel is transmitted.

17. The method of any of claims 3 to 16, wherein each of the basis functions is determined based on time-domain realizations of a filtered quasi-periodic delay-Doppler domain delta function defined by a delay period and a Doppler period.

18. The method of any of claims 3 to 16, wherein each of the basis functions is determined based on a lattice in a delay-Doppler domain, defined by a delay period (^^^) and a Doppler period (^^^), which consists of a single quasi-periodic localized pulse region of the delay-Doppler defined by 0 ^ ^^ ^ ^^^ and 0 ^ ^^ ^ ^^^.

19. The method of claim 17 or 18, wherein the delay period is greater than or equal to the expected maximum delay spread and the Doppler period is greater than or equal to the expected 182120091.2International Patent Application 119314.8125.WO00 maximum Doppler spread.

20. The method of any of claims 1 to 19, wherein the signal waveforms are generated using a Zak transformation.

21. The method of any of claims 1 to 19, wherein the signal waveforms are generated using a filter bank.

22. The method of any of claims 3 to 21, wherein the plurality of channel sensing signal transmissions are assigned to the plurality of inter-tile spacings based on a latency budget for a corresponding channel that is being sensed.

23. The method of claim 22, wherein the expected maximum delay spread and the expected maximum Doppler spread are configured in proportion to the latency budget.

24. The method of any of claims 3 to 23, wherein a user of the at least two users of the multiple users is configured to: receive the one or more parameters associated with the resource tile allocated to the user; configure, using the one or more parameters, a transceiver of the first user; and using the transceiver to perform a transmission or a reception in the resource tile.

25. The method of claim 24, wherein the transmission or the reception uses one or more data frames, and wherein configuring the transceiver comprises: configuring duration and bandwidth parameters of each of the one or more data frames based on the expected maximum delay spread or the expected maximum Doppler spread.

26. A digital communication apparatus comprising at least one processor, wherein the at least one processor is configured to cause the digital communication apparatus to implement the method of any of claims 1 to 25.

27. A computer-readable medium having code stored thereon, the code, upon execution by at least one processor, causing the at least one processor to control a digital communication apparatus to perform the method recited in any of claims 1 to 25. 182120091.2

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