Reference signal package for wireless communications

Abstract

In a wireless communication network, a pilot signal is sent on a wireless communication channel by determining a maximum delay spread for the transmission channel, determining a maximum Doppler spread for the transmission channel, and allocating a transmission resource set in the time-frequency domain to multiple pilot signals based on the maximum delay spread and the maximum Doppler spread.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This patent document claims priority to U.S. Provisional Application No. 62 / 303,318, filed on March 3, 2016, and U.S. Provisional Application No. 62 / 299,985, filed on February 25, 2016. The entire contents of all patent applications mentioned are incorporated herein by reference. Technical Field

[0003] The present invention relates to the field of telecommunications, and in particular to the estimation and compensation of impairments in telecommunication data channels. Background Art

[0004] Due to the explosive growth in the number of wireless user devices and the amount of wireless data that these devices may generate or consume, the bandwidth of current wireless communication networks is quickly exhausted, making it difficult to accommodate this rapid growth in data traffic and provide high-quality services to users.

[0005] The telecommunications industry has made various efforts to come up with next generation wireless technologies that can meet the performance demands of wireless devices and networks. Summary of the invention

[0006] Various techniques for pilot packing are disclosed, such as assigning transmission resources for transmission to multiple pilot signals. The disclosed techniques provide various operational advantages, including, for example, pilot packing by staggering pilots to achieve improved inter-pilot spacing, providing multiple pilots commensurate with a target delay-Doppler spread to be combated in a wireless channel, thereby optimally using available transmission bandwidth, and the like.

[0007] In one exemplary aspect, a wireless communication method is disclosed. Using the method, pilot data is sent over a wireless communication channel by determining a maximum delay spread for a transmission channel, determining a maximum Doppler spread for the transmission channel, and allocating a set of transmission resources in the time-frequency domain to a plurality of pilot signals based on the maximum delay spread and the maximum Doppler spread.

[0008] On the other hand, a wireless communication method includes determining a maximum delay spread for a transmission channel, determining a maximum Doppler spread for the transmission channel, multiple pilot signals that can be sent using a two-dimensional transmission resource set based at least on the maximum delay spread and the maximum Doppler spread, allocating a transmission resource set from the two-dimensional resource set to the multiple pilots, and sending the pilot signals on a wireless communication channel using the transmission resources.

[0009] In yet another aspect, a wireless communication device is disclosed, including a memory, a processor, and a transmitter. The wireless communication device may implement any of the above methods and other related technologies described herein.

[0010] A more detailed description of these and other aspects is provided herein. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 An exemplary trace of a time-varying impulse response for an accelerating reflector is shown;

[0012] Figure 2 An example of a delay-Doppler table for an accelerating reflector channel is shown;

[0013] Figure 3 Depicted are exemplary abstraction layers: (i) actual channel with signaling waveform, (ii) signaling in the time-frequency domain, (iii) delay-Doppler domain;

[0014] Figure 4 shows examples of notations used to represent signals at various stages of a transmitter and a receiver;

[0015] Figure 5 Depicts an example of a conceptual implementation of the Heisenberg transform in the transmitter and the Wigner transform in the receiver;

[0016] Figure 6 shows the g for OFDM system tr (t) and g r (t) An example of cross-correlation between;

[0017] Figure 7 Examples of information symbols in the information (delay-Doppler) domain (right) and corresponding basis functions in the time-frequency domain (left) are shown;

[0018] Figure 8 An example of a one-dimensional multipath channel is shown: (i) a sampling frequency response of Δf = 1 Hz, (ii) a periodic Fourier transform with a period of 1 / Δf = 1 s, (iii) a sampled Fourier transform with a period of 1 / Δf and a resolution of 1 / MΔf;

[0019] Fig. 9 An example of a one-dimensional Doppler channel is shown: (i) T s =1s sampling frequency response, (ii) period is 1 / T s =1Hz periodic Fourier transform, (iii) period 1 / T s And the resolution is 1 / NT s The sampled Fourier transform of

[0020] Fig.10 depicts an example of a time-varying channel response in the time-frequency domain;

[0021] Fig.11An exemplary SDFT of the channel response - (τ,ν) delay-Doppler domain is depicted;

[0022] Fig.12 An exemplary SFFT of the (τ,ν) delay-Doppler domain of the channel response-samples is depicted;

[0023] Fig.13 An example of the transformation from the time-frequency plane to the Doppler-delay plane is depicted;

[0024] Fig.14 depicts an example of discrete pulses used for channel estimation in the OTFS domain;

[0025] Fig.15 shows an example of different basis functions across the entire time-frequency frame assigned to different users;

[0026] Fig.16 An exemplary implementation of multiplexing three users in the time-frequency domain is shown;

[0027] Fig.17 An exemplary implementation of interleavingly multiplexing three users in the time-frequency domain is shown;

[0028] Fig.18 An example of an OTFS architecture block diagram is shown;

[0029] Fig.19 An example of a tf pilot grid (1902) superimposed on a data grid (1904) (N=14, M=2) is shown;

[0030] Fig. 20 An example of an OTFS-based pilot is shown, [a] shows 10 pilots on the delay-Doppler plane associated with the data plane, [b] shows Fig.19 tf data grid on A sample of the real part of Fig.19 a representation of the same 10 pilots on the delay-Doppler plane associated with a coarse pilot grid (N=14, M=2) of tf, and d shows a sample of the real part of P3 on the tf pilot grid;

[0031] Fig.21 An example of 4x2 pilots in a staggered structure on the delay-Doppler plane is shown;

[0032] Fig. 22 An example of a pilot grid (N=28, M=1) superimposed on a data grid is shown;

[0033] Fig.23 An exemplary implementation of 12 pilot grids (N=28, M=12) superimposed on a data grid is shown;

[0034] Fig.24 An exemplary implementation of 2 pilot grids (N=28, M=2) superimposed on a data grid is shown;

[0035] Fig.25 An example of UL (2502) and DL (2504) pilot sample points on a data grid (2506) is shown;

[0036] Fig.26 The pilot grid with N=28 and M=1 is shown in FIG. Fig.25 An example of packaging 10x4=40 pilots on a delay-Doppler plane associated with a grid of 2504 points;

[0037] Fig. 27 An example of a ring is shown;

[0038] Fig.28 An example of a sampled delay-Doppler plane is shown, which displays the absolute value of an instance of the time domain cyclic shift portion of 4 LTE UL DM RSs;

[0039] Fig.29 Shows Fig.28 An exemplary staggered version of the four LTE DM RSs shown in FIG.

[0040] Fig.30 The receiver input SNR is 50dB. Fig.28 (3004) and Fig.29 (3002) is a graphical depiction of an example of the estimated average SNR of 4 ETU-50 channels for 4 DM RSs;

[0041] Fig.31 An example of sampling points (3102) of a pilot on a data grid (3104) is shown;

[0042] Fig.32 An exemplary communication network in which the disclosed technology may be implemented is shown;

[0043] Fig.33 A flow chart illustrating an exemplary method of wireless communication;

[0044] Fig.34 is a block diagram of an example of a wireless communication device;

[0045] Fig.35 A flowchart illustrating an exemplary method of wireless communication; and

[0046] Fig.36 is a block diagram of an example of a wireless communication device that can be used to implement some of the techniques disclosed herein. DETAILED DESCRIPTION

[0047] Section headings are used in this article to help improve readability, but the scope of the technology discussed in each section is not limited to that section. Moreover, for the convenience of explanation, many simplifying assumptions are made. Although these simplifying assumptions are used to help convey concepts, they are not used to limit.

[0048] Some of these simplifying assumptions are as follows:

[0049] 1. Introduction

[0050] 4G wireless networks have served the public well, providing ubiquitous access to the Internet and enabling the proliferation of mobile applications, smartphones, and sophisticated data-intensive applications such as mobile video. It continues a proud tradition of cellular technology evolution, with each new generation bringing tremendous benefits to the public and enabling amazing improvements in productivity, convenience, and quality of life.

[0051] Looking ahead to the demands of all kinds of growing data usage being placed on the network, it is clear to the industry that the current 4G network will not be able to support the short-term demands for the foreseeable future. Data traffic has and continues to grow exponentially. AT&T reports that its network has seen a 100,000% increase in data traffic between 2007-2015. Looking ahead, the expansion of new applications such as immersive reality, remote robotics (touch screen internet), and mobile video is expected to overwhelm the carrying capacity of current systems. One of the goals of 5G system design is to be able to economically scale the network to 750Gbps / sq.Km in dense urban environments, however, today's technology is unable to achieve this.

[0052] In addition to the large amount of data, the quality of data transmission needs to be improved in the next generation system. The public has become accustomed to the ubiquity of wireless networks and requires an unfettered wired experience. It translates into a 50+Mbps requirement at every location (cell edge), which requires the implementation of advanced interference suppression techniques.

[0053] Another aspect of user experience quality is mobility. The throughput of current systems decreases significantly with increasing mobile speeds due to the Doppler effect which makes MIMO capacity gains vanish. Future 5G systems aim to increase supported speeds to not only 500Km / h for high-speed trains and aviation, but also to support many new automotive applications for vehicle-to-vehicle and vehicle-to-infrastructure communications.

[0054] While supporting growing, higher quality data services is necessary for the network to continue to support user demand, operators are also exploring new applications that allow new revenue and innovative use cases. The examples of automotive and smart infrastructure applications discussed above are one of several examples. Other examples include the deployment of public safety ultra-reliable networks, the use of cellular networks to support the end of the PSTN, etc. However, the biggest profit opportunity is arguably the deployment of a large number of networked devices, also known as the Internet of Things (IoT). However, current networks are not designed to support very large numbers of connected devices because each device has very low traffic in this case.

[0055] In summary, current LTE networks cannot achieve the cost / performance targets required to support the above goals, which necessitates a new generation of networks involving advanced PHY technologies. As discussed below, there are many technical challenges to be overcome in 5G networks.

[0056] 1.1 4G Technical Challenges

[0057] To allow machine-to-machine communication and realize the Internet of Things, the spectral efficiency of short bursts and the energy consumption of these devices must be improved (allowing 10 years of operation equivalent to 2AA batteries). In current LTE systems, network synchronization requirements place a burden on devices that are almost continuously on. In addition, efficiency decreases as the utilization of each UE (user equipment or mobile device) decreases. The PHY requirements for strict synchronization between the UE and the eNB (evolved Node B, or LTE base station) must be relaxed, allowing a redesign of the MAC of the loT connection to simplify the transition from the idle state to the connected state.

[0058] Another important use case for Cellular IoT (CloT) is deep building penetration to sensors and other devices, which requires an additional 20dB or more of dynamic range. 5G CloT solutions should be able to coexist with traditional high-throughput applications by dynamically adjusting parameters based on application context.

[0059] The path to higher spectral efficiency points to a larger number of antennas. Much research effort has gone into full-dimensional and massive MIMO architectures with good results. However, the benefits of larger MIMO systems may be hindered by the increased overhead of training, channel estimation, and channel tracking for each antenna. PHYs that are robust to channel variations and innovative ways to reduce the overhead of channel estimation are needed.

[0060] Robustness to time variations is often associated with challenges in high Doppler use cases such as vehicle-infrastructure and vehicle-vehicle automotive applications. With the expected use of spectrum up to 60GHz for 5G applications, Doppler effects are an order of magnitude higher than current solutions. The ability to handle mobility at these higher frequencies will be very valuable.

[0061] 1.2 OTFS-based solution

[0062] OTFS is a modulation technique that modulates (e.g., QAM) each information symbol to one of a set of two-dimensional (2D) orthogonal basis functions that span the bandwidth and duration of a transmission burst or packet. In particular, the set of modulation basis functions is derived to best represent the dynamics of a time-varying multipath channel.

[0063] OTFS transforms the time-varying multipath channel into a time-invariant delay-Doppler two-dimensional convolutional channel. In this way, it eliminates the difficulty in tracking time-varying fading, such as in high-speed vehicular communications.

[0064] OTFS increases the coherence time of the channel by several orders of magnitude. It simplifies the signaling on the channel by using the well-studied AWGN code for the average channel SNR. More importantly, it allows linear scaling of the throughput with the number of antennas in mobile vehicle applications due to the inherently accurate and efficient estimation of the channel state information (CSI). In addition, since the delay-Doppler channel representation is very compact, OTFS allows beamforming of massive MIMO and CSI at the transmitter of four, eight or more antennas in mobile vehicle applications. The CSI information required in OTFS is part of what is needed to track time-varying channels.

[0065] In deep building penetration use cases, one QAM symbol can be extended to multiple time and / or frequency points. This is a key technology to increase processing gain and building penetration capabilities for CloT deployments and PSTN replacement applications. Extensions in the OTFS domain allow expansion to wider bandwidths and durations while maintaining static channels that do not need to be tracked over time.

[0066] Loose synchronization: CoMP and network MIMO technologies have strict clock synchronization requirements for cooperating eNBs. If the clock frequencies are not well synchronized, each signal received by the UE from each eNB will have a significant "Doppler" frequency shift. Reliable signaling of OTFS over severe Doppler channels can minimize the associated synchronization difficulties while allowing CoMP deployment.

[0067] These benefits of OTFS will become apparent once the basic concepts behind OTFS are understood. There is a rich mathematical foundation for OTFS that leads to several variations, for example it can be combined with OFDM or multi-carrier filter banks. In this paper, we illustrate the challenges of balancing universality in the following order for ease of understanding.

[0068] In Section 2, we start by describing the wireless Doppler multipath channel and its effect on multicarrier modulation.

[0069] In Section 3, we develop OTFS as a modulation that matches the characteristics of time-varying channels. We illustrate OTFS in two processing steps:

[0070] The step of allowing transmission in the time-frequency plane via an orthogonal waveform generated by conversion of time and / or frequency in such a way that the (time-varying) channel response is sampled at multiple points in the time-frequency plane;

[0071] A pre-processing step using carefully crafted orthogonal functions in the time-frequency plane is used, which transform the time-varying channels in the time-frequency plane into time-invariant channels in the new information domain defined by these orthogonal functions.

[0072] In Section 4, we develop some more intuition about the new modulation scheme by exploring the behavior of the channel in the new modulation domain in terms of coherence, time and frequency resolution.

[0073] In Sections 5 and 6, we explore various aspects of channel estimation and multiplexing multiple users in the new information domain, respectively, while in Section 7 we address complexity and implementation issues.

[0074] In Section 8, we provide some performance results and put OTFS modulation into the context of cellular systems, discussing its properties and its benefits for 5G systems.

[0075] 2. Wireless Channel

[0076] The multipath fading channel is usually modeled in baseband as a convolutional channel with a time-varying impulse response

[0077]

[0078] Where s(t) and r(t) represent the complex baseband channel input and output, respectively. is the complex baseband time-varying channel response.

[0079] Although general, this expression does not give us any insight into the behavior and variability of the time-varying impulse response. A more useful and elegant model, also commonly used for a Doppler multipath double-fading channel, is

[0080] r(t)=∫∫h(τ,v)e j2πv(t-τ) s(t-τ)dvdτ (2)

[0081] In this expression, the received signal is a superposition of reflected copies of the transmitted signal, each delayed by the delay path τ, frequency-shifted by the Doppler frequency v, and weighted by the time-invariant delay-Doppler impulse response h(τ,ν) of these τ and v. In addition to the intuitiveness of this expression, equation (2) also maintains the generality of equation (1). In other words, it can represent complex Doppler trajectories such as accelerating vehicles, reflectors, etc. If we express the time-varying impulse response as a Fourier expansion with respect to the time variable t, we see

[0082]

[0083] Substituting (3) into (1), in some operations 1 We then obtain equation (2). More specifically, we obtain y(t) = ∫∫e j2πντ h(τ,v)e j2πv(t-τ) x(t-τ)dvdτ, which differs from the above equation by the exponential factor; however, we can absorb the exponential factor in the definition of the impulse response h(τ,v), making the two expressions equivalent.

[0084] As an example, Figure 1 shows the time-varying impulse response of the accelerating reflector in the (τ, t) coordinate system, and Figure 2 It is shown that the same channel is represented as a time-invariant impulse response in the (τ, v) coordinate system.

[0085] The important feature revealed by these two figures is how compact the (τ, v) expression is compared to the (τ, t) expression. This has important implications for channel estimation, equalization, and tracking as discussed later.

[0086] Note that although h(τ,v) is effectively time-invariant, the operation on s(t) is still time-varying, as can be seen from the action of an explicit, complex exponential function of time in equation (2). Technical efforts in this paper focus on developing modulation schemes based on appropriate selection of orthogonal basis functions that render the channel truly time-invariant in the domain defined by these basis functions. Let us motivate those efforts with a high-level outline of the structure of the scheme proposed here.

[0087] Let us consider a set of orthogonal basis functions φ indexed by τ,v that are orthogonal to translation and modulation τ,ν (t), that is

[0088]

[0089] Let us consider the transmitted signal as a superposition of these basis functions

[0090] s(t)=∫∫x(τ,ν)φ τ,ν (t)dτdv (5)

[0091] where the weight x(τ,v) represents the information-bearing signal to be transmitted. After the transmitted signal of (5) passes through the time-varying channel of equation (2), we obtain the superposition of the delayed version and the modulated version of the basis function, which is obtained by (4)

[0092] r(t)=∫∫h(τ,v)ej2πv(t-τ) s(t-τ)dνdτ

[0093] =∫∫φ τ,v (t){h(τ,v)*x(τ,v)}dτdv (6)

[0094] where * denotes a two-dimensional convolution. Equation (6) can be considered as a generalization of the derivation of the convolution relation for linear time-invariant systems using one-dimensional exponentials as basis functions. Note that the terms in brackets can be obtained at the receiver by τ,ν (t) is restored using matched filtering. In this way, a two-dimensional channel relationship y(τ,ν)=h(τ,v)*x(τ,v) is established in the (τ,ν) domain, where y(τ,v) is the output of the receiver's two-dimensional matched filter. Also note that in this domain the channel is described by a time-invariant two-dimensional convolution.

[0095] This final different interpretation of the wireless channel is also very useful in the following text. Think of s(t) and r(t) as square-integrable functions The elements of the Hilbert space of . Equation (2) can be interpreted as acting on the input s(t) A linear operator of , parameterized by the impulse response h(τ,v) and producing an output r(t):

[0096]

[0097] Note that although the operator is linear, it is not time-invariant. In the Doppler-free case, i.e., if h(v,τ) = h(0,τ)δ(v), then equation (2) reduces to a time-invariant convolution. Also note that although for a time-invariant system the impulse response is parameterized in one dimension, in the time-varying case we have a two-dimensional impulse response. Although in the time-invariant case the convolution operator produces a superposition of delays of the input s(t), (hence the parameterization is along a one-dimensional delay axis) in the time-varying case we have a superposition of delay and modulation operations as seen in equation (2) (hence the parameterization is along two-dimensional delay and Doppler axes). This is the main difference that makes the time-varying expression non-commutative (as opposed to the convolution operation which is commutative), and complicates the treatment of time-varying systems.

[0098] The important thing about equation (7) is that the operator Π h (·) can be compactly parameterized in two-dimensional space h(τ,v) and provides an effective time-invariant description of the channel. Typical channel delay spread and Doppler spread are a very small fraction of the symbol duration and subcarrier spacing of a multicarrier system.

[0099] In mathematical literature, the time-varying system representation of (2) and (7) is called the Heisenberg representation [1]. It actually shows that every linear operator (7) can be parameterized by an impulse response as in (2).

[0100] 3. OTFS modulation over Doppler multipath channels

[0101] The time variation of the channel introduces significant difficulties in wireless communications related to channel acquisition, tracking, equalization, and transmission of channel state information (CSI) to the transmit side for beamforming and MIMO processing. In this paper, we develop a modulation domain based on a set of standard orthogonal basis functions through which we can transmit information symbols and through which the information symbols can experience a static time-invariant two-dimensional channel for the duration of a packet or burst transmission. In this modulation domain, the channel coherence time is increased by several orders of magnitude and the problems associated with channel fading in the time or frequency domain in SISO or MIMO systems are significantly reduced.

[0102] Orthogonal Time-Frequency-Space (OTFS) modulation consists of a cascade of two transforms. The first transform maps the two-dimensional plane (also called the Delay-Doppler plane) where the information symbols are located to the time-frequency plane. The second transform transforms the time-frequency domain into the waveform time domain that constructs the actual transmitted signal. This transform can be considered a generalization of multi-carrier modulation schemes.

[0103] Figure 3 A diagram of the two transforms that make up OTFS modulation is provided. It shows the high-level signal processing steps required at the transmitter and receiver. It also includes the parameters that define each step, which will become apparent as we further reveal each step. In addition, Figure 4 Block diagrams of the different processing stages at the transmitter and receiver are shown and notations for the various signals are created.

[0104] We begin our description with the transform that relates the waveform domain to the time-frequency domain.

[0105] 3.1 Heisenberg transformation

[0106] Our goal in this section is to construct an appropriate transmit waveform that carries the information provided by the symbols on a grid in the time-frequency plane. We develop this modulation scheme to transform the channel operation into an equivalent operation in the time-frequency domain and has two important properties:

[0107] The channels are orthogonal on the time-frequency grid;

[0108] Channel time variations are simplified on a time-frequency grid and can be accounted for using additional transforms.

[0109] Fortunately, these goals can be achieved with a scheme that is very close to known multi-carrier modulation techniques as described below. We start with a general framework for multi-carrier modulation and then give examples of OFDM and multi-carrier filter bank implementations.

[0110] Let us consider the following components of time-frequency modulation:

[0111] The grid or grid on the time-frequency plane, that is, the sampling of the time axis sampling period T and the frequency axis sampling period Δf:

[0112]

[0113] a packet burst with total duration NT(s) and total bandwidth MΔf(Hz);

[0114] We want to send a modulation symbol set X[n,m], n = 0, ..., N-1, m = 0, ..., M-1 through this burst;

[0115] It has the property of being orthogonal to the translation T and the modulation Δf 2 The transmission pulse g tr (t):

[0116]

[0117] Given the above components, the time-frequency modulator is a Heisenberg operator on the grid Λ, i.e., it is modulated via a pulse waveform g tr The superposition of the delay and modulation operations on (t) maps the two-dimensional symbol X[nm] to the transmitted waveform

[0118]

[0119] More formally

[0120]

[0121] We use Π X (·) denotes the “discrete” Heisenberg operator and is parameterized by the discrete values ​​X[n,m].

[0122] Note the similarity of (11) to the channel equation (7). This is not accidental, but because we apply a modulation effect that mimics the channel effect, so that the end effect of the cascade of modulation and channel is more easily controlled at the receiver. This is common practice; for example, the simplest form of linear modulation (for a time-invariant channel) is the convolution of the transmit pulse g(t) with a triangular train of QAM information symbols sampled at baud rate T:

[0123]

[0124] In our use case, for a time-varying channel, we convolve and modulate the transmit pulse (refer to channel equation (2)) with a two-dimensional triangular column sampled in the video domain at a specific baud rate and at the carrier interval.

[0125] Sampling rate and pulse g in the time-frequency domain tr The bandwidth and duration (i.e., time-frequency localization) of (t) are related. In order for the orthogonality condition of (9) to hold for frequency separation Δf, the time interval must be T ≥ 1 / Δf. The critical sampling case of T = 1 / Δf is generally not achievable and refers to the extreme case, e.g., OFDM systems with cyclic prefix length 0 and g tr (t) is the filter bank of the ideal Nyquist pulse.

[0126] Some examples are:

[0127] Example 1: OFDM Modulation : Let us consider a system with M subcarriers and symbol length T OFDM , cyclic prefix length T CP and subcarrier spacing 1 / T OFDM OFDM system. If we set the symbol duration T = T OFDM +T CP , number of symbols N = 1, subcarrier spacing Δf = 1 / T OFDM and constrains the duration of the subcarrier to a square window g of symbol length T tr (t)

[0128]

[0129] Substituting into equation (10), we obtain the OFDM formula 3

[0130]

[0131] Example 2: Single Carrier Modulation : If we substitute M = 1 subcarrier, T equals the baud period, and g tr (t) is equal to the square root raised cosine Nyquist pulse, then equation (10) is reduced to single carrier modulation.

[0132] Example 3: Multi-Carrier Filter Bank (MCFB) :If g tr (t) is a square root raised cosine Nyquist pulse with excess bandwidth α, T is equal to the baud period Δf=(1+α) / T and, then equation (10) describes the MCFB.

[0133] It may be counter-intuitive to express the modulation operation as a Heisenberg transform as in equation (11). We usually think of modulation as a transformation of modulation symbols X[m,n] to a transmitted waveform s(t). Instead, the Heisenberg transform uses X[m,n] as the weights / parameters of the operator, which is applied to the prototype transmit filter response g tr (t) - yields s(t) when referred to equation (11). Although counter-intuitive, this formula is very useful in pursuing the abstraction of the modulation-channel-modulation cascade effect in the two-dimensional domain where the channel can be described as time-invariant.

[0134] Next we turn our attention to the processing required at the receiver side to get from the waveform domain back to the time-frequency domain.Since the received signal undergoes two Heisenberg transforms (one by the modulation effects and the other by the channel effects), it is natural to ask what the end-to-end effects of this cascade are.

[0135] The answer to this question is given by the following result:

[0136] Argument 1 : The two Heisenberg transforms defined by equations (7) and (2) are parameterized by the impulse responses h1(τ,ν) and h2(τ,ν) and applied in cascade to the waveform So

[0137]

[0138] Here, h(τ,v)=h2(τ,ν)⊙h1(τ,v) is the “twisted” convolution of h1(τ,v) and h2(τ,v) defined by the following convolution and modulation operations:

[0139] h(τ,ν)=∫∫h2(τ′,v′)h1(τ-τ′,vv′)e j2πv′(τ-τ′)t dτ′dv′ (16)

[0140] prove :See Appendix 0.

[0141] Applying the above results to the concatenation of the modulation and channel Heisenberg transforms of (11) and (7), the received signal is given by the Heisenberg transform

[0142] r(t)=Π f (g tr (t))+v(t)=∫∫f(τ,v)e j2πτ(t-τ) g tr (t-τ)dvdτ+v(t) (17)

[0143] where v(t) is the additive noise and f(τ,v), the impulse response of the combined transform is given by the twisted convolution of X[n,m] and h(τ,v)

[0144]

[0145] This result can be considered as an extension of the single carrier modulation case, where the signal received over a time-invariant channel is given by the convolution of the QAM symbol with a composite pulse, which is the convolution of the transmitter pulse and the channel impulse response.

[0146] With this result established, we can look at the receiver processing steps.

[0147] 3.2 Receiver Processing and Wigner Transform

[0148] Typical communication system design dictates that the receiver perform a matched filtering operation, taking the inner product of the received waveform with a transmitter pulse appropriately delayed or distorted by the channel. In our case, we have used a collection of delayed and modulated transmit pulses, and we need to perform matched filtering on each pulse. Figure 5 provides a conceptual view of the process. At the transmitter, we modulate a set of M subcarriers for each symbol we transmit, and at the receiver, we perform matched filtering on each of these subcarrier pulses. We define the receiver pulse g r (t) and taking the inner product with the set of its delayed and modulated versions. The receiver pulse g r (t) are in many cases identical to the transmitter pulse, but we keep different notations to cover some cases where they are different (most notably in OFDM where the CP samples are dropped).

[0149] Although this approach will produce sufficient statistics for data detection in the ideal channel case, what may be of interest here is the case of non-ideal channel effects. In this case, sufficient statistics for symbol detection are obtained by matched filtering with channel-distorted, information-carrying pulses (assuming the additive noise is white Gaussian noise). However, in many well-designed multi-carrier systems (e.g., OFDM and MCFB), the channel-distorted version of each subcarrier signal is just a scalar version of the transmitted signal, allowing a filter design that is independent of the channel and uses the matched on-carrier pulses originally transmitted. We will later make these statements more precise and investigate whether the conditions required for this case are true.

[0150] Figure 5is only a conceptual illustration and does not point to an actual implementation at the receiver. Typically, this matched filtering is implemented in the digital domain using FFT or polyphase transforms for OFDM and MCFB respectively. In this article, we are more interested in understanding the principles of this modulation. To do this, we will do this by taking the inner product of the received waveform with a delayed and modulated version of the receiver pulse at a random time and frequency offset. <g r (t-τ)e j2πν(t-τ) ,r(t)>Consider this generalization of matched filtering. Although this is not a practical implementation, it allows us to Figure 5 The operation can be viewed as a two-dimensional sampling of the more general inner product.

[0151] We define the inner product as

[0152]

[0153] Known function A gr,r (τ,ν) is the mutual ambiguity function of the radar and the mathematical community and produces a matched filter output when sampled with τ = nT, ν = mΔf (on the grid Λ), that is,

[0154]

[0155] In mathematics, the fuzzy function is related to the inverse of the Heisenberg transform, the Wigner transform. Figure 5 This provides intuitive feel, making the receiver appear to be the inverse of the sender's operations. 4 .

[0156]

[0157] The key question here is how the matched filter output Y[n,m] (more generally Y(τ,v)) is related to the transmitter input X[n,m]. We have already established in (17) that the matched filter input r(t) can be expressed as a Heisenberg expression with an impulse response f(τ,v) (plus noise). The output of the matched filter then has two contributions

[0158] The last term is the noise contribution, which we express as The first term on the right is the matched filter output of a (noise-free) input consisting of a superposition of delayed and modulated versions of the transmitted pulse. Next we establish that: This term can be expressed as a warped convolution of the two-dimensional impulse response f(τ,v) with the mutual ambiguity function (or two-dimensional cross-correlation) of the transmitted and received pulses.

[0159] The following rationale summarizes the key results.

[0160] Principle 1 :(Basic time-frequency domain channel equation). If the received signal can be expressed as

[0161] Π f (g tr (t))=∫∫f(τ,v)e j2πv(t-τ) g tr (t-τ)dvdτ (22)

[0162] Then the mutual ambiguity between this signal and the received pulse can be expressed as

[0163]

[0164] prove :See Appendix 0.

[0165] Recall from (18), f(τ,v) = h(τ,ν)⊙X[n,m], that is, the composite impulse response is the distorted convolution of itself, the channel response, and the modulation symbol.

[0166] Substituting f(τ,v) from (18) into (21), we obtain the end-to-end channel description in the time-frequency domain:

[0167] where V(τ,v) is an additive noise term. Equation (24) provides an abstraction of a time-varying channel in the time-frequency plane. It shows that the output of the matched filter at any time and frequency point (τ,v) is given by the delayed Doppler impulse response of the channel warped convolution of the impulse response of the modulation operator with the warped convolution of the mutual ambiguity (or two-dimensional cross-correlation) of the transmitted and received pulses.

[0168] Evaluate equation (24) on the grid Λ to obtain the matched filter output modulation symbol estimate

[0169]

[0170] To make equations (24) and (25) more intuitive, we first consider the case of an ideal channel, i.e., h(τ,v) = δ(τ)δ(v). In this case, by directly substituting, we obtain the convolution relationship

[0171] To simplify equation (26), we use the orthogonality property of the ambiguity function. Since we use different transmit and receive pulses, we modify the orthogonality condition of the transmit pulse design described in (9) to a biorthogonality condition

[0172]

[0173] Under this condition, only one term remains in (26) and we obtain

[0174] Y[n,m]=X[n,m]+V[n,m] (28)

[0175] where is white noise with V[n,m] added. Equation (28) shows that the matched filter output recovers the transmitted symbols (with noise added) under ideal channel conditions. Of course, of greater interest is the case of irrational time-varying channel effects. Next we show that even in this case, channel orthogonality is maintained (no inter-symbol or inter-carrier interference), while the channel complex gain distortion has a closed-form solution.

[0176] The following principle summarizes the result as a generalization of (28).

[0177] Principle 2 : (end-to-end time-frequency domain channel equation):

[0178] If h(τ,ν) has the max ,v max ) and if A gr,gtr (τ,v)=0,τ∈(nT-τ max ,nT+τ max )、v∈(mΔf-v max ,mΔf+v max ), that is, the biorthogonality property of the ambiguity function of (27) is true at least in the neighborhood of each grid point (mΔf,nT) of the grid Λ as large as the support of the channel response h(τ,v), then the following equation holds

[0179] Y[n,m]=H[n,m]X[n,m]

[0180] H[n,m]=∫∫h(τ,ν)e j2πνnT e -j2π(v+mΔf)τ dνdτ (29)

[0181] If the blur functions are only approximately biorthogonal in a (continuous) neighborhood of Λ, then (29) is only approximately true.

[0182] prove :See Appendix 0.

[0183] Equation (29) is the basic equation describing the channel behavior in the time-frequency domain. It is the basis for understanding the nature of the channel and its changes along the time and frequency dimensions.

[0184] Now some observations about equation (29) are in order. As mentioned before, there is no interference between X[n,m], regardless of time n or frequency m.

[0185] The end-to-end channel distortion in the modulation domain is a (complex) scalar quantity that needs to be equalized.

[0186] If there is no Doppler, that is, h(τ,ν)=h(τ,0)δ(v), then equation (29) becomes

[0187]

[0188] This is a known multi-carrier result, with each sub-carrier symbol being multiplied by the frequency response of the time-invariant channel evaluated at the frequency of that sub-carrier.

[0189] If there is no multipath, that is, h(τ,ν) = h(0,ν)δ(τ), then equation (29) becomes

[0190] Y[n,m]=X[n,m]∫h(v,0)e j2πvnT dτ (31)

[0191] Note that each subcarrier experiences a complex expression as a weighted superposition of exponentials for fading as a function of time nT. This is a major complexity in the design of wireless systems with mobility such as LTE, which necessitates pilot transmission and continuous tracking of the channel, which becomes increasingly difficult with higher vehicle speeds or Doppler bandwidths.

[0192] We end this section with some examples of this general framework.

[0193] Example 3 : (OFDM modulation). In this case the basic transmit pulse is given by (13) and the basic receive pulse is

[0194]

[0195] That is, the receiver zeroes the CP samples and applies a square window to the symbols including the OFDM symbols.In this case, it makes no sense that the biorthogonal property holds exactly along the time dimension. Figure 6 The cross-correlation between the transmitted and received pulses of (13) and (32) is shown. Note that the cross-correlation is exactly 1 and 0 near 0 and ±T, respectively, and is CP Therefore, as long as the support of the channel in the time dimension is less than T CP , then the biorthogonality condition is satisfied along the time dimension. Since the ambiguity takes a sinusoidal function as a function of frequency and is not equal to 0 in the entire support of the Doppler spread, the condition is only approximate in the frequency dimension.

[0196] Example 4 : (MCFB modulation). In the case of a multi-carrier filter bank g tr (t) = g r(t) = g(t). There are several designs of the base pulse g(t). The square root raised cosine pulse provides good localization along the frequency dimension at the expense of less localization along the time dimension. If T is much larger than the support of the channel in the time dimension, each subchannel sees a flat channel and the biorthogonal property is approximately maintained.

[0197] In summary, in this section we described one of the two transformations that define OTFS. We explained how the transmitter and receiver can apply appropriate operators to the basis transmit and receive pulses and make the channel orthogonal according to equation (29). We further saw by example how the choice of basis pulses affects the time and frequency localization of the transmitted modulation symbols and the quality of the achieved channel orthogonality. However, equation (29) shows that the channel in this domain suffers from fading in the time and frequency dimensions via a complex superposition of linear phase factors in the absence of inter-symbol interference.

[0198] In the following sections, we will start from equation (29) and describe the second transform that defines OTFS; we will show how this transform defines the information domain for which the channel does not fade in either domain.

[0199] 3.3 2D OTFS Transform

[0200] Note that the time-frequency response H[n,m] in equation (29) is related to the channel delay-Doppler response h(τ,v) by an expression similar to that of the Fourier transform. However, there are two important differences: (i) the transform is two-dimensional (along delay and Doppler) and (ii) the exponents defining the transform in the two dimensions have opposite signs. Despite these difficulties, equation (29) points to the use of complex exponentials as basis functions for modulating the information symbols and simply transmitting the superposition of these modulated complex exponential bases in the time-frequency domain. This is the approach we will pursue in this section.

[0201] This is similar to the SC-FDMA modulation scheme where in the frequency domain we send a superposition of modulated indices (the output of the DFT pre-processing block). The reason we pursue this direction is to exploit the Fourier transform properties and convert a multiplicative channel in one Fourier domain into a convolutional channel in another Fourier domain.

[0202] Given the difficulties with equation (29) mentioned above, we need to develop a suitable version of the Fourier transform and the associated sampling theory results. We start with the following definitions:

[0203] Definition 1 : Symplectic Discrete Fourier Transform : Given a square-integrable two-dimensional sequence We define

[0204]

[0205] Note that the 2D Fourier transform above (known as the Symplectic Discrete Fourier Transform in the mathematical community) differs from the more well-known Cartesian Fourier transform in that the exponential function in each of the two dimensions has opposite signs. This is necessary in this case because it matches the behavior of the channel equation.

[0206] Also note that the resulting x(τ,ν) is periodic with (1 / Δf, 1 / T). This transformation defines a new two-dimensional plane, which we call the Delay-Doppler plane and can exhibit the maximum delay 1 / Δf and the maximum Doppler 1 / T. One-dimensional periodic functions are also called functions on a circle, while 2D periodic functions are called functions on a torus. In this case, x(τ,v) is defined on a torus with circumference (dimensions) (1 / Δf, 1 / T).

[0207] The periodicity of x(τ,ν) (or the sampling rate in the time-frequency plane) also defines a grid in the delay-Doppler plane, which we call the inverse grid

[0208]

[0209] The points on this inverse grid have the property of yielding the exponent in (33), an integer multiple of 2π.

[0210] The inverse transform is given by:

[0211]

[0212] Where c = TΔf.

[0213] Next we define a sampled version of x(τ,v). Specifically, we want to take M samples in the delay dimension (spaced 1 / MΔf) and N samples in the Doppler dimension (spaced 1 / MΔf). More formally, we define a dense version of the inverted grid as

[0214]

[0215] Make We define a discrete periodic function on this dense grid with period (1 / Δf, 1 / T), or equivalently we define the function on a discrete torus with these dimensions

[0216]

[0217] These functions are related to discrete periodic functions on the grid Λ, or equivalently, to functions on a discrete annulus, via the Fourier transform relation

[0218] Z0={(nT,mΔf),m=0,…,M-1,n=0,…N-1,} (38)

[0219] We wish to develop an expression for sampling Eq. (33) on the grid of (37). First, we start with the following definitions.

[0220] Definition 2 : Symplectic Finite Fourier Transform : If X p [k,l] takes (N,M) as the period, so we define

[0221] Note x p [m,n] also has a period of [M,N], or equivalently, it is in the discrete ring Formally, SFFT(X[n,m]) is Linear transformation of .

[0222] Now we consider generating x p [m,n] is the sampled version of (33), that is, Then we can show that (39) still holds for X p [m,n] is the periodic position of X[n,m] with period (N,M)

[0223]

[0224] This is similar to the known result that sampling in one Fourier domain is aliased in the other domain.

[0225] The inverse discrete (symplectic) Fourier transform is given by

[0226]

[0227] where l = 0, ..., M-1, k = 0, ..., N-1. If the support of X[n,m] is limited to the time-frequency of Z0 (no aliasing in (40)), then X p [n,m]=X[n,m], n,m∈Z0, and the inverse transform (41) restores the original signal.

[0228] In the mathematical community, the SDFT is called "discrete" because it represents the signal using a discrete set of exponents, and the SFFT is called "finite" because it represents the signal using a finite set of exponents.

[0229] Arguably, the most important property of the symplectic Fourier transform is that it transforms multiplicative channel effects in one domain into circular convolution effects in the transformed domain. It is summarized in the following argument.

[0230] Argument 2 :set up is a periodic 2D sequence. Then

[0231] SFFT(X1[n,m]*X2[n,m])=SFFT(X1[n,m])·SFFT(X2[n,m]) (42)

[0232] Where * represents two-dimensional circular convolution.

[0233] prove :See Appendix 0.

[0234] With this framework created, we are ready to define the OTFS modulation.

[0235] Discrete OTFS modulation: Consider a set of NM QAM information symbols x[l,k] arranged on a 2D grid that we wish to send, with k = 0, ..., N-1, l = 0, ..., M-1. We consider x[l,k] to have a two-dimensional periodicity with a period of [N,M]. In addition, assume that the multicarrier modulation system is defined by the following terms:

[0236] The grid on the time-frequency plane, i.e., the sampling of the time axis with a sampling period T and the frequency axis with a sampling period Δf (refer to equation (8));

[0237] A packet burst with a total duration NT s and a total bandwidth MΔf Hz;

[0238] The transmitted and received pulses g satisfy the biorthogonal property of (27) tr (t),

[0239] Transmit windowed square integrable function multiplied by modulation symbols in the time-frequency domain

[0240] Through the set of basic functions b k,l [n,m] is a set of modulation symbols X[n,m] associated with information symbol x[k,l], n=0,…,N-1, m=0,…,M-1

[0241]

[0242] The basic function b k,l [n,m] is related to the inverse symplectic Fourier transform (see equation (41)).

[0243] Given the above components, we define the discrete OTFS modulation in the following two steps:

[0244] X[n,m]=W tr [n,m]SFFT -1 (x[k,l])

[0245] s(t)=Π X(g tr (t)) (44)

[0246] The first equation in (44) describes the OTFS transform, which combines an inverse symplectic transform domain windowing operation. The second equation is expressed by g parameterized by X[n,m] tr The Heisenberg transform of (t) describes the transmission of the modulation symbols X[n,m]. A more explicit formulation of the modulation step is given by equations (41) and (10).

[0247] Although the expression of the OTFS modulation via the symplectic Fourier transform reveals important properties, it is easier to understand the modulation via equation (43), i.e., by modulating the 2D basis function b in the time-frequency plane k,l [n,m] to send each information symbol.

[0248] Figure 7 This explanation is visualized by isolating each symbol in the information domain and showing its contribution to the time-frequency modulation domain. Of course, the transmitted signal is a superposition of all symbols on the right (information domain) or all basis functions on the left (modulation domain).

[0249] Figure 7 For all Use slim window W tr [n,m] = 1, the others are 0. This may seem redundant, but this window has a technical reason: recall that SFFT -1 (x[k,l]) is a periodic sequence that extends to infinite time and bandwidth. By applying a window, we restrict the modulation symbols to the finite time and bandwidth available. The window generally extends beyond the period of the information symbol [M,N] and can have shapes other than rectangular pulses. This can be similar to adding cyclic prefixes / suffixes in the time and frequency dimensions and be shaped or unshaped. The choice of window has implications for the shape and resolution of the channel response in the information domain, which we discuss later. It also has implications for receiver processing because, as we will see next, potential cyclic prefixes / suffixes must be removed or processed.

[0250] Discrete OTFS demodulation: Assume that the transmitted signal undergoes channel distortion according to (7) and (2), resulting in r(t) at the receiver. In addition, let the receiver adopt the receive windowed square integrable function W r [n,m]. Then, the modulation operation consists of the following steps:

[0251] Match filtering the received pulse, or more formally, evaluating the ambiguity function (Wigner transform) on Λ to obtain an estimate of the time-frequency modulation symbol;

[0252]

[0253] Windowing and periodization of Y[n,m]

[0254]

[0255] And in the periodic sequence Y p Apply the symplectic Fourier transform on [n,m]

[0256]

[0257] The first step of the modulation operation can be interpreted as a matched filter operation in the time-frequency domain, as we discussed before. The second step is to ensure that the SFFT is a periodic sequence. This step can be skipped if a thin window is used. The third step can also be interpreted as the projection of the time-frequency modulation symbols onto the orthogonal basis functions.

[0258]

[0259] The discrete OTFS modulation defined above points to an efficient implementation via a discrete-periodic FFC-type process. However, it does not provide insight into the temporal and bandwidth resolution of these operations in the context of two-dimensional Fourier sampling theory. We next introduce continuous OTFS modulation and relate the more practical discrete OTFS as a sampled version of the continuous modulation.

[0260] Continuous OTFS modulation: Consider a two-dimensional periodic function with period [1 / Δf, 1 / T] that we wish to transmit. The choice of period may seem arbitrary at this point, but it will become clear after the discussion in the following sections. Furthermore, assume that the multicarrier modulation system is defined by:

[0261] The grid on the time-frequency plane, i.e., the sampling of the time axis with a sampling period T and the frequency axis with a sampling period Δf (refer to equation (8));

[0262] The transmitted and received pulses satisfy the biorthogonal property of (27)

[0263] Multiply by the transmit windowing function of the modulation symbols in the time-frequency domain

[0264] Given the above components, we define the continuous OTFS modulation via the following two steps:

[0265] X[n,m]=W tr [n,m]SDFT -1 (x(τ,ν))

[0266] s(t)=Π X (g tr (t)) (49)

[0267] The first equation describes the inverse discrete time-frequency sigmoid Fourier transform (see equation (35)) and the window function, while the second equation describes the transmission of the modulation symbols via the Heisenberg transform (see equation (10)).

[0268] Continuous OTFS demodulation: Assume that the transmitted signal s(t) undergoes channel distortion according to (7) and (2), resulting in r(t) at the receiver. In addition, assume that the receiver adopts the receive windowing function The demodulation operation then consists of two steps:

[0269] Evaluate the ambiguity function (Wigner transform) on Λ to obtain an estimate of the time-frequency modulation symbol

[0270]

[0271] Window the modulation symbols and apply the symplectic Fourier transform to them:

[0272]

[0273] Note that since the SDFT is defined on a non-periodic square-integrable sequence, there is no periodization of Y[n,m] in (50) and (51). The periodization step required for discrete OTFS can be understood as follows. Suppose we wish to recover the transmitted information symbols by performing continuous OTFS demodulation followed by sampling on a delay-Doppler grid.

[0274]

[0275] Since it is impractical to perform a continuous sigmoid Fourier transform, we consider whether the same result can be obtained using the SFFT. It turns out that if the input sequence is first periodicized (aliased) - see also (39)(40), then the SFFT process will produce exactly the samples we seek.

[0276] We have now described Figure 3 All the steps of OTFS modulation are described in . We also discussed how the Wigner transform at the receiver inverts the Heisenberg transform at the transmitter (see equations (26), (28)), and similarly for the forward and inverse sigmoid Fourier transforms. The key question is what form the end-to-end signal relationship takes when a non-ideal channel is located between the transmitter and the receiver. The answer to this question is given below.

[0277] 3.4 Channel equations in OTFS domain

[0278] The main conclusion of this section shows how the time-varying channels in (2) and (7) can be transformed into time-invariant convolutional channels in the delay-Doppler domain.

[0279] Argument 3 : Consider a set of NM AQM information symbols arranged in a 2D periodic sequence x[l,k] with period [M,N]. The sequence x[l,k] undergoes the following transformation:

[0280] It is modulated using discrete OTFS modulation of equation (44).

[0281] It is distorted by the delay-Doppler channel of equations (2) and (7).

[0282] It is demodulated by discrete OTFS demodulation of equations (45) and (47).

[0283] The estimated sequence obtained after demodulation is The input QAM sequence x[m,n] and the windowed impulse response h w The sampled version of the two-dimensional periodic convolution of (·) gives

[0284]

[0285]

[0286] where h w (τ′,ν′) represents the circular convolution of the channel response and the windowing function 5

[0287] h w (τ′,v′)=∫∫e -j2πvτ h(τ,v)w(v′-τ,v′-v)dτdν (54)

[0288] where the windowing function w(τ,ν) is the symplectic Fourier transform of the time-frequency window W[n,m]

[0289]

[0290] and where W[n,m] is the product of the send window and the receive window.

[0291] W[n,m]=W tr [n,m]W r [n,m] (56)

[0292] Proof: See Appendix 0.

[0293] In many cases, the windows in the sender and receiver match, i.e., W tr [n,m]=W0[n,m] and Therefore W[n,m]=|W0[n,m]| 2 .

[0294] The effect of windowing is to produce a blurred version of the original channel, whose resolution depends on the span of available frequency and time samples as discussed in the following sections. If we consider a rectangular (or elongated) window, i.e., W[n,m] = 1, n = 0, ..., N-1, m = -M / 2, ..., M / 2-1 and others are 0, then its SDFT w(τ, v) in (55) is a two-dimensional Dirichlet kernel with a bandwidth inversely proportional to N and M.

[0295] There are several other uses for window functions. Systems can be designed with window functions whose purpose is to randomize the phase of transmitted symbols and are similar to how QAM symbol phases are randomized in WiFi and multimedia coax multimedia communication systems. This randomization is more important for pilot symbols than for the data carrying symbols. For example, if adjacent cells use different window functions, the problem of pilot contamination can be avoided.

[0296] The different uses of the window are the ability to implement random access systems via OTFS using spread spectrum / CDMA type techniques which will be discussed later.

[0297] 4. Channel time / frequency coherence and OTFS resolution

[0298] In this section, we investigate some OTFS design issues, such as the choice of data frame length, bandwidth, symbol length, and number of subcarriers. We study the trade-offs between these parameters and gain more understanding of the capabilities of the OTFS technique.

[0299] Since OTFS is based on Fourier expression theory similar spectrum analysis concepts apply, such as frequency resolution vs Fourier transform length, sidelobes vs windowing shape, etc. One distinction that can be a source of confusion comes from the naming of the two Fourier transform domains in the current framework.

[0300] OTFS transforms the time-frequency domain into the delay-Doppler domain and establishes the Fourier pair: (i) time Doppler; and (ii) frequency Delay. The "spectral" resolution of interest here is either in the Doppler dimension or in the delay dimension.

[0301] These issues can be more easily clarified by example. Let us consider a time-invariant multipath channel (0 Doppler) with frequency response H(f,0) for all t. Figure 8 In the first plot we show the real part of H(f,0) and its sampled version on a grid of M=8 subcarriers. Figure 8The second plot of shows the SDFT of the sampled H(mΔf,0), i.e., h(τ,0) along the delay domain. Note that taking this frequency response to the “delay” domain reveals the structure of this multipath channel, i.e., the presence of two reflectors of equal power in this example. Also, note that due to the nature of the Discrete Fourier Transform, the delay dimension of the SDFT is periodic with a period of 1 / Δf as expected. Finally, in Figure 8 In the third plot of , we show the SFFT of the frequency response, which, as expected, is a sampled version of the SDFT of the second plot. Note that the SFFT has M = 8 points in each period 1 / Δf, which results in a resolution of 1 / MΔf = 1 / BW in the delay domain.

[0302] In the current example, the reflectors are separated by more than 1 / MΔf and are resolvable. If not, the system would experience a flat channel within the observed bandwidth and the two reflectors would blur into one reflector in the delay domain.

[0303] Fig. 9 Similar results are shown for a flat Doppler channel with a time-varying frequency response H(0,t) for all f. The first plot shows the response as a function of time, while the second plot shows the SDFT along the Doppler dimension. Finally, the third plot shows the SFFT, a sampled version of the transform. Note that the SDFT is periodic with a period of 1 / T while the SFFT is periodic with a period of 1 / NT and has a resolution of .

[0304] Available from Fig. 9 The conclusion is that as long as there is sufficient variation in the channel over the observation time NT, that is, as long as the reflectors have a Doppler frequency difference greater than 1 / NT, the OTFS system will resolve these reflectors and produce an unfaded equivalent channel in the delay-Doppler domain. In other words, OTFS can take a channel that inherently has a coherence time of only T and produce an equivalent channel with a coherence time NT in the delay-Doppler domain. This is an important property of OTFS because it can increase the coherence time of the channel by several orders of magnitude and allow MIMO processing and beamforming under Doppler channel conditions.

[0305] Two examples of one-dimensional channels that we investigate are Fig.10 This is a special case of a more general two-dimensional channel. The time-frequency response and its sampled version are shown in this figure, where the sampling period is (T, Δf). Fig.11 The SDFT of this sampled response across the Doppler and delay dimensions respectively is shown, which is periodic with a period of (1 / T, 1 / Δf).

[0306] We now investigate the Nyquist sampling requirements for this channel response. 1 / T is generally of the same order as Δf (for an OFDM system with zero-length CP, it is exactly 1 / T = Δf), so Fig.11 The period of the channel response in is roughly (Δf,T). As long as the support of the channel response is less than ±Δf / 2 in the Doppler dimension and less than ±T / 2 in the delay dimension, aliasing can be avoided.

[0307] Fig.12 shows the SFFT, i.e. Fig.11 A sampled version of . Fig.11 The resolution in the Doppler dimension and delay dimension is 1 / NT and 1 / MΔf respectively.

[0308] We are Fig.13 The sampling aspects of OTFS modulation are summarized in . OTFS modulation consists of two steps shown in this figure:

[0309] The Heisenberg transform converts the time-varying convolution channel in the waveform domain into an orthogonal but time-varying channel in the time-frequency domain. For the entire bandwidth BW and M subcarriers, the frequency resolution is Δf = BW / M. For the frame duration T f and N symbols, with a time resolution of T = T f / N.

[0310] The SFFT transform converts the time-varying channel in the time-frequency domain into a time-invariant channel in the delay-Doppler domain. The Doppler resolution is 1 / T f , the delay resolution is 1 / BW.

[0311] The choice of window provides a trade-off between mainlobe width (resolution) and sidelobe suppression, as in classical spectrum analysis.

[0312] 5. Channel Estimation in OTFS Domain

[0313] Channel estimation schemes can be designed in many different ways for OTFS system channels, with many different implementation options and details. In this section we only give a high-level summary and highlight the key concepts.

[0314] A straightforward way to perform channel estimation requires sending a sounding OTFS frame containing discrete trigonometric functions in the OTFS domain or equivalently sending a set of unmodulated carriers in the time-frequency domain, which may be modulated with a known symbol such as BPSK that is removed at the receiver as is common in many OFDM systems. This approach can be considered an extension of the channel estimation symbols used in WiFi and coaxial multimedia modems. Fig.14 An OTFS symbol containing this pulse is shown.

[0315] However, this approach can be wasteful because the extension of the channel response is only a fraction of the entire extension of the OTFS frame (1 / T, 1 / Δf). For example, in LTE systems, 1 / T ≈ 15 kHz and the maximum Doppler shift f d,max Typically 1 to 2 orders of magnitude smaller. Similarly, 1 / Δf ≈ 67 microseconds, and the maximum delay spread τ max is also 1-2 orders of magnitude smaller. Therefore, the region of the OTFS frame that we can dedicate to channel estimation is smaller, while the rest of the frame carries useful data. More specifically, for a channel with support (±f d,max ,±τ max ) channel, we need a length of (2f d,max / T,2τ max / Δf) of OTFS subframe.

[0316] In the case of multi-user transmission, each UE may have its own channel estimation subframe located in a different part of the OTFS frame. This is similar to the multiplexing of multiple users when sending uplink sounding reference signals in LTE. The difference is that OTFS benefits from the benign effects of its two-dimensional nature. For example, if τ max is 5% of the extension of the delay dimension and f d,max It is 5% of the Doppler dimension, so the channel estimation subframe only requires 5% x 5% = 0.25% of the OTFS frame.

[0317] Note that although the channel estimation symbols are confined to a small portion of the OTFS frame, they actually probe the entire time-frequency domain via the corresponding basis functions associated with these symbols.

[0318] A different approach to channel estimation is to dedicate pilot symbols on a sub-grid in the time-frequency domain. This is analogous to the CRS pilots in the downlink LTE sub-frame. The key issue with this approach is to determine the density of pilots sufficient to be used for channel estimation without introducing aliasing. Assume that the pilots occupy the sub-grid (n0T,m0Δf), for some integers n0,m0. Recall that for this grid, the SDFT is periodic with a period of (1 / n0T,1 / m0Δf). Then, applying the aliasing results discussed previously to this grid, we obtain the alias-free Nyquist channel support region (±f d,max ,±τ max ) = (±1 / 2n0T, ±1 / 2m0Δf). The density of pilots can then be determined by this relationship that gives the maximum support for the channel. The pilot sub-grid should extend over the entire time-frequency frame so that the resolution of the channel does not need to be compromised.

[0319] 6.OTFS-Access: Multiplexing of more than one user

[0320] There are many ways to multiplex several uplink or downlink transmissions in one OTFS frame. This is a rich topic and its full treatment is beyond the scope of this article. Here we will briefly review the following multiplexing methods:

[0321] OTFS delay-Doppler domain multiplexing

[0322] Multiplexing in the time-frequency domain

[0323] Multiplexing of code extension domain

[0324] Multiplexing in the spatial domain

[0325] Delay-Doppler Domain Multiplexing : This is the most natural multiplexing scheme for downlink transmission. Different users are given different sets of OTFS basis functions, information symbols or resource blocks. Given the orthogonality of the basis functions, the users can be separated at the UE receiver. The UE only needs to demodulate the part of the OTFS frame that is relevant to it.

[0326] This approach is similar to the allocation of PRBs to different UEs in LTE. One difference is that in OTFS, even a small subframe or resource block in the OTFS domain will be transmitted through the entire time-frequency frame via the basis function and will experience the average channel response. Fig.15 This is illustrated by showing the different basis functions belonging to different users. Thus, no compromise on channel resolution is required for each user, regardless of resource block or subframe size.

[0327] In the uplink direction, transmissions from different users experience different channel responses. Therefore, different subframes in the OTFS domain will experience different convolution channels. This can potentially introduce inter-user interference at the edge where two user subframes are adjacent and require a guard gap to eliminate the inter-user interference. To prevent this overhead, different multiplexing schemes can be used in the uplink, as explained next.

[0328] Multiplexing in the time-frequency domain : In this method, resource blocks or subframes are allocated to different users in the time-frequency domain. Fig.16 This is illustrated for a three user case. User 1 (blue 1602) occupies the entire frame length but only half of the available subcarriers. User 2 and User 3 (red 1604 and blue 1606, respectively) occupy the other half of the subcarriers, dividing the total length of the frame between them.

[0329] Note that in this case, each user employs a slightly different version of the OTFS modulation described in Section 3. One difference is that each user i receives a i ,M i ), N i ≤N,M i≤ M. This reduces the resolution of the channel, in other words reduces the range of variations that each user in the time-frequency plane will experience in its channel. On the other hand, this also gives the scheduler an opportunity to schedule users in the best part of the channel in the time-frequency plane.

[0330] If we want to extract the maximum diversity of the channel and distribute users across the entire time-frequency frame, we can multiplex the users by interleaving. In this case, one user occupies a sub-sampling grid of the time-frequency frame, while another user occupies another sub-sampling grid adjacent to it. Fig.17 The same three users as before are shown but interleaved in the subcarrier dimension. Of course, interleaving in the time dimension and / or in both dimensions is also possible. The grid used for each user, or the degree of interleaving, is only limited by the channel spread we need to handle.

[0331] Multiplexing in the Time-Frequency Spreading Code Domain :Suppose we wish to design a random access PHY and MAC layer in which users can access the network without having to go through elaborate RACH and other synchronization procedures. There has been some discussion on the need for such a system to support Internet of Things (IoT) deployments. Each user is assigned a different two-dimensional window function, where the two-dimensional window function is designed as a random generator. The windows of different users are designed to be approximately orthogonal to each other and to time and frequency shifts. Each user then transmits on only one or a few basis functions and uses the window as a means of randomizing interference and providing processing gain. This can result in a very simplified system that may be attractive for low-cost, short-burst IoT applications.

[0332] Multiplexing in the spatial domain Finally, similar to other OFDM multi-carrier systems, a multi-antenna OTFS system can support multiple users transmitting over the entire time-frequency frame based on the same basis function. The users are separated by appropriate transmitter and receiver beamforming operations. However, a detailed treatment of the MIMO-OTFS architecture is beyond the scope of this paper.

[0333] 7. Implementation Issues

[0334] OTFS is a novel modulation technique with many benefits and a strong mathematical foundation. From an implementation standpoint, its additional benefit is compatibility with OFDM and requires only incremental changes in the transmitter and receiver architecture.

[0335] Recall that OTFS consists of two steps. The Heisenberg transform (from the time-frequency domain to the waveform domain) is already implemented in today's systems in the form of OFDM / FDMA. In the conception of this paper, this corresponds to the prototype filter g(t) for square pulses. Other filtered OFDM and filter bank variations have been proposed for 5G, which can also be included in this general framework through different choices of g(t).

[0336] The second step of OTFS is the two-dimensional Fourier transform (SFFT). It can be considered as Fig.18 The pre-processing and post-processing steps at the transmitter and receiver respectively are shown in . In this sense, from an implementation point of view, it is similar to the SC-FDMA pre-processing step.

[0337] From a complexity comparison point of view, we can calculate the complexity for a frame of N OFDM symbols with M subcarriers, SC-FDMA adds N DFTs with M points for each (assuming the worst case M subcarriers given a single user). Then the additional complexity of SC-FDMA is NMlog2(M) over the baseline OFDM architecture. For OTFS, the 2D SFFT has complexity NMlog2(NM)=NMlog2(M)+NMlog2(N), so the term NMlog2(M) is the additional complexity of OTFS compared to SC-FDMA. For an LTE subframe with M=1200 subcarriers and N=14 symbols, the additional complexity is 37% larger than that of SC-FDMA.

[0338] Note also that, from an architectural and implementation point of view, OTFS increases the PHY capabilities of the existing LTE modern architecture and does not introduce coexistence and compatibility issues.

[0339] 8. Exemplary Benefits of OTFS Modulation

[0340] OTFS modulation has many benefits tied to the challenges that 5G systems are trying to overcome. Arguably the biggest benefit and main reason to study this modulation is its ability to communicate over a channel that fades in the time-frequency frame but still provides a stationary, deterministic, and unfaded channel interaction between the transmitter and receiver. In the OTFS domain, all information symbols experience the same channel and the same SNR.

[0341] In addition, OTFS makes optimal use of fading and power fluctuations in the received signal to maximize capacity. To illustrate this, assume that the channel consists of two reflectors that introduce peaks and valleys in the channel response in time or frequency or both. OFDM systems can theoretically solve this problem by allocating power resources according to the water filling theory. However, due to practical difficulties, these methods have not been continued in wireless OFDM systems, resulting in a wasted portion of the time-frequency frame with excess received energy, which is followed by other portions with low received energy. The OTFS system will determine the two reflectors and the receiver equalizer will use the coherent combination of the energy of the two reflectors, providing a non-fading channel with the same SNR for each symbol. Therefore, it provides channel interaction, which is designed to maximize capacity under the transmission assumption of allocating the same power across symbols (common in existing wireless systems) by using only standard AWGN codes.

[0342] Additionally, OTFS provides a domain in which the channel can be characterized in a very compact form. This has important implications for solving the channel estimation bottleneck that plagues current multi-antenna systems, and may be the key to addressing similar problems in further massive MIMO systems.

[0343] One benefit of OTFS is its ability to easily handle extreme Doppler channels. We have verified two and four stream MIMO transmissions in fields 2x2 and 4x4, respectively, in a vehicle setting moving at 90Km / h. It is not only useful in vehicle-to-vehicle, high-speed trains, and other Doppler-sensitive 5G applications, but is also an enabling technology for mmWave systems where the Doppler effect will be significantly simplified.

[0344] In addition, OTFS provides a natural way to apply spreading codes, transmit processing gain, and CDMA random access multi-carrier systems based on spread spectrum. It eliminates the time and frequency fading common to multi-carrier systems and simplifies the maximum ratio combining subsystem. The processing gain addresses the deep building penetration challenges required for IoT and PSTN replacement applications, while the CDMA multi-access solution addresses the battery life challenges and short burst efficiency required for IoT deployments.

[0345] Last but not least, the compact channel estimation process provided by OTFS may be necessary for the successful deployment of advanced technologies such as coordinated multi-point (Co-MP) and distributed interference mitigation or network MIMO.

[0346] Appendix 0

[0347] Proof of Argument 1 :set up

[0348] g1(t)=∫∫h1(τ,v)e j2πv(t-τ) g(t-τ)dvdτ (57)

[0349] g2(t)=∫∫h2(τ,v)e j2πvb(t-τ) g1(t-τ)dvdτ (58)

[0350] Substituting (58) into (57), we obtain after some manipulations

[0351] g2(t)=∫∫f(τ,v)e j2πv(t-τ) g(t-τ)dvdτ (59)

[0352] where f(τ,v) is given by (16).

[0353] Proof of Principle 1 : The principle can be proved by defining the following equation and then by a straightforward but tedious substitution on the left-hand side of (23):

[0354]

[0355] By changing the order of integration and the integration variable (t-τ′)→t, we obtain

[0356] in

[0357]

[0358] Note that the second line on the right hand side of (61) is exactly the right hand side of (23), which we shall prove.

[0359] Proof of Principle 2 : Substituting into (23) and evaluating on the grid Λ, we obtain

[0360]

[0361] By using the biorthogonality condition in (63), only one term remains on the right hand side and we obtain the desired result of (29).

[0362] Proof of Argument 2 :Based on the definition of SFFT, it is not difficult to prove that the delay is converted into linear phase

[0363]

[0364] Based on this result, we can evaluate the SFFT of circular convolution

[0365]

[0366] Produces the desired result.

[0367] Proof of Argument 3: We have shown that in the time-frequency domain we have a multiplicative frequency-selective channel given by (29). This result, combined with the convolutional and multiplication properties of the symplectic Fourier transform (see Argument 1 and Eq. (42)), yields the desired result.

[0368] Specifically, if we substitute Y(n,m) into the demodulation equation (48) from the time-frequency channel equation (29) and substitute X[n,m] into (29) from the modulation equation (43), we obtain the (complex) end-to-end expression

[0369]

[0370] Considering the factors in brackets as the discrete symplectic Fourier transform of W(n,m), we have

[0371] Further considering the double integral as the convolution of the channel impulse response (multiplied by the exponential) with the transformed window, we obtain

[0372]

[0373] This is the desired result.

[0374] 9. Reference signal

[0375] Unless specifically stated otherwise, the terms reference signal and pilot signal are used interchangeably herein.

[0376] 9.1 Reference Signal Based on OTFS

[0377] Assume a time-frequency (tf) grid defined by the following discrete points

[0378]

[0379] where dt (seconds) and df (Hz) are the physical distances between grid points in the time and frequency dimensions respectively, and K and L are integers 6. We call this grid the data grid, since most points on this grid will be occupied by data samples. Reference signals (pilots) will occupy a subset of the data grid. When pilot samples occupy a regular subset of the data grid, they form a regular (coarse) pilot grid defined by

[0380]

[0381] As an example, for N=14, M=2, the tf plane looks like Fig.19 shown.

[0382] As described herein, the data grid (69) is related to the delay-Doppler (τ,v) ring by a sigmoid Fourier transform, which respectfully has the following delay and Doppler circles:

[0383]

[0384] The delay-Doppler ring associated with the (coarse) pilot grid (70) is a ring with a smaller circumference

[0385]

[0386] It can be shown that the 2D function x(τ,ν) on the continuous delay-Doppler circle associated with the tf grid defined in (69) can be transformed into a 2D discrete function X[i,j] on the tf grid by the inverse symplectic discrete Fourier transform defined as

[0387]

[0388] If the pth pilot x p (τ,ν) is chosen as the trigonometric function δ(τ) on the delay-Doppler circle. p ,ν p ), then the expression for this pilot on the time-frequency grid defined in (69) will be

[0389]

[0390] Fig. 20 An example of positioning 10 OTFS based pilots in the delay-Doppler plane and how one of these pilots looks after it has been subjected to an inverse symplectic discrete Fourier transform (71) is shown.

[0391] Each OTFS-based reference signal is generated at different points (τ p ,v p ) are placed on the delay-Doppler circle. The sum of these trigonometric functions is then transformed to the tf plane using an inverse symplectic discrete Fourier transform, and a subset of samples in the tf plane is selected to be transmitted. In other words, the OTFS-based reference signal is a symplectic index that is limited to a subset of points on the data grid.

[0392] If the P pilots are transmitted using a subset of the data grid forming a regular grid as presented in (70), then the tf samples for the n pilots are:

[0393]

[0394] Where N and M are fixed positive integers representing the coarse pilot grid size.

[0395] When the pilot samples in the tf plane form a regular grid, the number of pilots that can be packed into the grid can be calculated based on the circumference of the ring associated with the pilot grid and the maximum delay and Doppler spread of the channel that each pilot is expected to experience. To avoid leakage between pilots, the maximum number of pilots that can be packed into each dimension is the circumference of the ring divided by the maximum spread. Note that the delay and Doppler spread are calculated as respects Δ τ and Δ ν , the maximum number of pilots that can be packed in each dimension is

[0396]

[0397] As an example, for a signal with an average maximum delay spread of 5 μs and a maximum Doppler frequency of 50 Hz (maximum Doppler spread of 100 Hz), a delay circle and Doppler circle The ring of can support up to 13 pilots in the delay dimension and 2 pilots in the Doppler dimension, for a total of 26 pilots. How close the system can get to the maximum achievable pilot packing will depend on the pilot observation window. The finite observation window of the pilot translates into convolving the pilot in the delay-Doppler plane with the sine Fourier transform of the window (which is a two-dimensional sine function in the case of a rectangular window). Therefore, a larger observation window will result in lower leakage between received pilots, allowing:

[0398] Improved accuracy of channel estimation; and

[0399] Tighter pilot packing, with a maximum number of pilots specified in an infinite window (74).

[0400] Note that staggering the pilots (eg, not placing them on a rectangular grid in the delay-Doppler plane) can improve the spacing between pilots, thus providing better, denser packing. Fig.21 An example of staggered pilots is shown. From the figure, it can be seen that all pilots are staggered. Examples of how staggered LTE UL DM reference signals can improve channel estimation are described herein.

[0401] 9.2 Reference Signal Packaging

[0402] Packing orthogonal OTFS-based pilots can be achieved using one of the following schemes:

[0403] Delay-Doppler Pilot Packing (DDPP): Arranges pilots in the delay-Doppler plane keeping a sufficiently large distance to minimize the leakage of the received pilots between each other after the worst-case delay and Doppler shift of the channel that each pilot may experience, and considers the impact of (sub-)sampling of pilots in the TF domain and the pilot observation window.

[0404] • Time Frequency Pilot Packing (TFPP): Assign each pilot (no overlap) a sufficiently coarse grid (with a regular pilot grid, the circumference of the associated ring must be larger than the expected maximum delay and Doppler shift through the channel) that can support the associated channel.

[0405] Fixed Pilot Package (MPP): A combination of DDPP and TFPP.

[0406] OTFS-based pilots can be packed very efficiently, thus supporting the simultaneous transmission of a very large number of orthogonal pilots without using a large percentage of the channel capacity.

[0407] Here are some pilot package examples:

[0408] Example 1 (DDPP)

[0409] Assume the following:

[0410] Data Grid Parameters (LTE Numerology)

[0411] οdt=1 / 14ms

[0412] οdf=15kHz

[0413] Channel parameters:

[0414] οDelay spread: 5μs (ETU)

[0415] οMaximum Doppler frequency: 50Hz (100Hz extension)

[0416] If we choose a pilot grid of N=28 (Ndt=2ms) and M=1, Fig. 22 M = 1, the circumference of the pilot ring will be

[0417]

[0418] The maximum number of pilots that can be supported in this configuration is 13x5=65. This is done by placing 13 pilots in the delay dimension of the ring (5.13 μs apart) and 5 replicas of these pilots in the Doppler dimension of the ring (100 Hz apart). In practice, for a 100 MHz channel bandwidth and allowing for windows of reasonable size in the time dimension, this configuration can support at least 40 pilots (10x4).

[0419] Example 2 (TFPP):

[0420] For the same data grid as in Example 1, assume the following channel parameters:

[0421] Delay spread: 5μs (ETU)

[0422] Maximum Doppler frequency: 200Hz (400Hz extended)

[0423] If we divide the pilot grid of Example 1 into Fig.23 If there are 12 different pilot grids represented by different colored gems in , each of these pilot grids will have N=28 (Ndt=2ms) and M=12 (Mdf=180KHz). The circumference associated with these grids will be:

[0424]

[0425] As can be seen from the circumference, each pilot grid can only support a single pilot, which can be Fig.23 The 12 pilot grid supports a total of 12 pilots.

[0426] Example 3 (MPP):

[0427] If we divide the grid of Example 1 into Fig.24 The two grids shown will each have Ndt = 2 ms and Mdf = 30 kHz. The rings associated with the two grids will have the following circumference:

[0428]

[0429] Assuming the same channel parameters as in Example 1, the maximum number of pilots that can be supported by each of these rings is 6x5=30, for a total of 60 pilots on both grids. For a 10MHz channel bandwidth and a window of reasonable size in the time dimension, a practical number of 40 (4x5x2) or 50 (5x5x2) pilots is expected.

[0430] Another example of MPP is described later in this document.

[0431] The advantages of using DDPP are that:

[0432] Provide more flexible support for different channel delays and Doppler spreads. For DDPP, pilots can be placed anywhere on a continuous ring, whereas when pilots are multiplexed in the time-frequency plane, the pilots are restricted to use a discrete grid.

[0433] Provides lower latency than TFPP when pilots are used to demodulate data, since the grid used for each pilot in TFPP is coarser, so the average time between the data and the last pilot used for insertion (the pilot following the data) is larger.

[0434] Since equivalent quality of channel estimation can be achieved with TFPPS using a shorter observation window as achieved with DDPP, there is an advantage when attempting to use a short pilot observation window with TFPP.

[0435] 9.3 Potential uses of OTFS-based reference signals in LTE

[0436] In order to support massive MIMO by using channel reciprocity, all active UEs need to send pilots on the UL so that the eNodeB can predict the channel for these UEs to precode their DL transmissions. This requires supporting a large number of pilots.

[0437] One way to support a large number of pilots is to send OTFS-based reference signals using resources allocated to the sounding reference signal (SRS). SRS in LTE systems is sent on the last symbol of the UL subframe. In TDD mode, SRS can be scheduled for the shortest configuration period, i.e., 5 subframes (5ms). For this configuration, SRS uses a pilot grid of N=70, M=1 (see Section 9.1). The ring associated with this grid respectfully has the following delayed Doppler circles:

[0438]

[0439] As an example, assuming an ETU channel with a maximum Doppler frequency of 10 Hz, the maximum number of pilots that can be supported on this grid is 13x10 = 130. For a practically limited observation window, with a sufficiently good channel prediction of 5 ms in the future (distance between pilots), the number of pilots that may be supported is less but still desirably very large.

[0440] 9.4 Examples of Reference Signals for 5G Communications

[0441] The proposed reference signal structure supports precoding for downlink (DL) transmission in the presence of time-varying channels by exploiting channel reciprocity. We refer to precoding as a generalized beamforming scheme that supports multi-layer transmission in MIMO systems.

[0442] For 5G reference signals, it is recommended that:

[0443] Dedicate a subset of the time-frequency data grid to the reference signal;

[0444] Using the OTFS-based reference signal described in Section 9.1;

[0445] Scramble the reference signal by multiplying its time-frequency samples by a 2D linear chirp sequence (e.g., 2D Zadoff-Chu) to limit inter-cell interference between the reference signals. A 2D sequence will have richer sequence selection than a unidimensional sequence due to good cross-correlation properties;

[0446] Packing all reference signals (pilots) required for the operation of the system on a grid dedicated to reference signals (except for a grid that may be used to demodulate reference signals that may be sent with data if needed);

[0447] Enable the eNodeB (base station) to continuously send DL reference signals on a dedicated time-frequency DL pilot grid;

[0448] • Make each UE (User Equipment) send its uplink (UL) reference signal on a dedicated UL pilot grid before the eNodeB starts precoding its transmissions to the UE.

[0449] Separating the pilot from the data allows the pilot transmission to start before the data transmission starts, which allows the receiver to use a large pilot observation window resulting in higher channel observation resolution. Higher channel observation resolution results in:

[0450] Better channel estimation;

[0451] Better pilot packing (due to reduced leakage between received pilots);

[0452] Improved channel predictability, which will improve precoding in the presence of Doppler spread,

[0453] All of this does not affect data transmission latency.

[0454] To be able to use channel reciprocity for precoding, the channel response information must be current within the DL transmission time. To achieve this, the eNodeB must regularly receive pilots from all active UEs so that the eNodeB has the latest channel information that needs to be sent to the UEs. It can be shown that using the proposed pilot grid that satisfies the conditions in (74) and has a sufficiently long observation window provides good channel prediction for precoding.

[0455] The number of pilots that need to be supported in the UL is equal to the number of active UEs in the cell and at the edges of adjacent cells (to minimize interference between pilots and allow support for interference cancellation in the DL) multiplied by the number of spatial multiplexing layers for each UE. For pilot transmission, the active UE will be the UE that starts sending or receiving data (optionally it can be the time to wake up to start sending or receiving data). At this point, the UE will start sending pilots. Until the eNodeB collects enough pilots from the UE to support precoding, the eNodeB sends data to the UE without precoding. Moreover, in order to limit the number of UEs that need to send pilots continuously, support for precoding for each UE can be configurable. In this case, the UE can only send demodulation pilots together with the data.

[0456] To support precoding on the DL, it is recommended to have active UEs send their pilots regularly. This allows the eNodeB to collect a history of pilot information from all active UEs. When a packet needs to be sent to a specific UE, the eNodeB can use the pilot history of that specific UE to calculate the precoder and apply it to the sent packet. In addition to using the pilots used to precode the DL transmission, the eNodeB can use the regularly sent UL pilots to estimate the channel for demodulating packets sent on the UL. Using the pilot history will also help improve the spacing of the desired pilot from other pilots and improve the quality of the channel estimate used to demodulate the received signal. It is assumed that the transmission on the UL is not precoded or the eNodeB is aware of the precoder used.

[0457] In DL, assuming that the precoding is good enough, the UE does not need a demodulation reference signal (DM RS) on the precoding layers. For this assumption, the eNodeB only needs to send reference signals on the spatial layers where precoding is not used. Therefore, the number of pilots on DL will be much smaller than the number of pilots on UL. It is recommended to send all DL pilots regularly. These pilots will be used by the UE as DM RS (for non-precoded transmissions) and for measuring observed time difference of arrival (OTDOA). If it is considered that DM reference signals are still needed after precoding, the DM reference signals can be sent together with the data.

[0458] The number of pilots that need to be supported in DL is equal to the number of unprecoded layers per cell multiplied by the number of neighboring cells. This is to prevent the pilots from interfering with the pilots of neighboring cells and to support the measurement of OTDOA.

[0459] 9.4.1 Downlink Reference Signal

[0460] For LTE numerology, it is recommended to use a pilot grid with N = 28 and M = 1. For an ETU channel with an average maximum Doppler frequency of 50 Hz (ETU-50), this will support up to 40 pilots, as shown in Example 1 in Section 9.2. If a smaller number of pilots is required, this grid will support a higher Doppler spread (e.g., for 20 pilots, the maximum Doppler frequency it can support is 100 Hz), and vice versa.

[0461] If the subcarrier spacing becomes 150KHz, the data grid parameters are:

[0462] dt = 1 / 140ms

[0463] df = 150KHz

[0464] For ETU-50 channels with the same pilot grid (N=28, M=1), this numerology also supports 40 pilots. In this case, all pilots are packed in the Doppler dimension.

[0465] The DL pilots shall be sent continuously on the pilot grid.The UE should collect a long enough history of the pilots to support a good enough channel estimate to receive non-precoded (data or control) transmissions from the eNodeB or to improve the measured TOA.

[0466] 9.4.2 Uplink Reference Signal

[0467] For LTE numerology, one or more adjacent pilot grids with N=28 and M=1, and / or one or more adjacent pilot grids with N=14 and M=1 are recommended. For ETU-50, each of the first grids will support a maximum of 40 pilots (as shown in Example 1 in Section 9.2), and each of the second grids will support 80 pilots. A good example is to use a combination of one grid with N=28, M=1 and one grid with N=14, M=1. For an ETU channel with an average Doppler frequency of 50 Hz, Fig.25 This example demonstrated in supports 120 UL pilots and 40 DL pilots. Fig.26 A representation of 40 evenly spaced pilots on the delay-Doppler plane associated with a pilot grid of is shown.

[0468] Fig.25 The pilot structure supports both symmetric and asymmetric DL / UL transmissions. Note that for this pilot structure, a switch guard period (GP) is required after each DL subframe. Therefore, the more asymmetric the transmission, the more switch guard periods (GP) are required. If the downlink to downlink switch point period is N subframes, then (N-1) GPs are required for N subframes.

[0469] Fig.25 The pilot structure of 160 pilots adds 14.3% (2 / 14) overhead to support 160 pilots. 0.09% overhead per pilot. Note that this overhead per pilot depends on the delay and Doppler spread of the channel. The number of pilots supported in this pilot configuration is doubled and for a maximum Doppler frequency of 25 Hz (instead of 50 Hz), the overhead per pilot will be halved.

[0470] 9.5 Comparison with LTE Pilot Packaging

[0471] As shown in Section 9.4.2, the reference signal structure recommended in Section 9.3 can accommodate 40 pilots on DL and 120 pilots on UL, which fully support ETU-50 channels. DL pilots use 3.6% of the total PHY resources (data grid) and UL pilots occupy 10.7% of the total PHY resources.

[0472] In LTE, cell-specific reference signals occupy 14.3% of the DL PHY resources. For these reference signals, LTE supports up to 40 unprecoded DL spatial layers. On the UL, to support 8 spatial layers, the UE can be configured (in TDD mode) to send SRS with a configuration period of 5ms. In this mode, a total of 8 SRS can be supported to support the ETU channel. These SRS occupy 1.43% of the UL PHY resources. These reference signals cannot support any significant Doppler spread in the ETU channel.

[0473] Table 1 below shows a summary of the comparison between the proposed reference signals and the LTE reference signals. Note that to support the lower Doppler channels for OTFS RS in the table, the number of OTFS RSs can be increased in proportion to the reduction in Doppler spread, or the overhead can be reduced in proportion. As an example, for an ETU-5 channel, the overhead of the OTFS RS can be increased by a factor of 10 (approximately 0.02% / RS) while still supporting 140 pilots on the DL and 20 pilots on the UL.

[0474] Table 1

[0475]

[0476] Appendix A - Mathematical Background

[0477] The function g of the discrete variable ndt is a one-dimensional grid The function of (set of integers) and (real number set). It is known that the Fourier transform of the discrete function g(ndt) is a continuous periodic function with a period of 1 / dt. The discrete Fourier transform transforms the function g(ndt) into a continuous function G(f), where f = [0,1 / dt). Since the discrete Fourier transform transforms the grid Λ t The product of the above two functions is transformed into a circular convolution, so it is convenient to say that G(f) lies on a circle with circumference 1 / dt.

[0478] Similar to the one-dimensional case, it can be shown that the discrete symplectic Fourier transform (a twisted version of the two-dimensional discrete Fourier transform) transforms a function g of two discrete transforms into a function of two continuous periodic variables. Assume that the function g is located on the following grid:

[0479]

[0480] The discrete symplectic Fourier transform of g(ndt,mdf) is given by:

[0481] SF(g)(τ,ν)=G(τ,ν)=dtdf·∑ n,m e -2πj(vndt-τmdf)g(ndt,ndf) (76)

[0482] The function G(τ,ν) lies on the two-dimensional plane τ×ν=[0,1 / df)x[0,1 / dt), or equivalently on a ring with circumference 1 / df in dimension τ and on a ring with circumference 1 / dt in dimension ν. The ring is called the grid Λ t,f Associated rings. Fig. 27 An example is depicted.

[0483] Appendix B - Effect of interleaving LTE UL DM reference signals

[0484] The uplink demodulation reference signal in LTE is composed of the base sequence r according to the following formula: uv The time domain cyclic shift τ(λ) of (k) is defined as:

[0485] r uv (mL RS + k, τ) = w m (λ)e jτ(λ)k r uv (k)|0≤k≤L RS -1,m=0,1 (77)

[0486] Among them, L RS is the length of the reference signal sequence (number of subcarriers), λ is the spatial layer index, [w0(λ)w1(λ)] = [±1±1] is the orthogonal cover code (OCC), and r uv (k) is the basis (Zadoff-Chu) sequence. jτ(λ)k represents the layer-dependent cyclic shift separated from the pilots of different layers. For rank-4 UL transmission, Fig.28 As shown, the 4UL reference signal can be represented in the delay-Doppler plane. Fig.28 It can be seen that all four reference signals have the same Doppler frequency shift. Fig.29 The staggered reference signals shown allow for better channel estimation when using a smaller number of PRBs (small observation window).

[0487] Appendix C MPP Example

[0488] By using the same numerology and channel parameters of Example 1 in Section 9.2, we select Fig.31 The red rows form the same ring as in Example 1 and can support a maximum of 65 pilots. The remaining red points can be viewed as 13 coarse grids, where N = 28 and M = 12 for each grid. The circumference of the ring associated with this grid is

[0489]

[0490] Since this ring supports 1x5 pilots, the total number of pilots that can be supported by these 13 coarse grids is 5x13=65. Fig.31 The maximum total number of pilots supported by the pilot sample points in is 130. A more practical number is 40 on the first grid (same as Example 1) and 4x13=52 on the coarse grid, for a total of 92 pilots.

[0491] For the same example, we can divide the pilot sample points differently into 25 grids, with N = 28 and M = 12. Each such grid supports a maximum of 1x5 pilots, for a total of 5x25 = 125 pilots; a more practical number of 4x25 = 100 pilots is supported.

[0492] Fig.32 An exemplary communication network in which the disclosed technology may be implemented is shown. The network 3200 may include a base station transmitter that transmits a wireless signal s(t) (a downlink signal) to one or more receivers r(t) that may be located in a variety of locations, including inside or outside a building or in a moving vehicle. The receivers may send uplink and downlink transmissions to a base station that is typically located near the wireless transmitter.

[0493] Fig.33 A flow chart of an exemplary method 3300 for wireless communication is shown. The method 3300 includes the following operations: (3302) determining a maximum delay spread for a transmission channel, (3304) determining a maximum Doppler spread for the transmission channel, (3306) allocating a set of transmission resources to a plurality of pilot signals in the time-frequency domain based on the maximum delay spread and the maximum Doppler spread, and (3308) sending the pilot signal on the wireless communication channel using the transmission resources. Various examples and options are disclosed herein in detail in Section 9.

[0494] In some implementations, each pilot signal may correspond to a trigonometric function in the delay-Doppler domain.

[0495] In some embodiments, the allocating operation 3306 may include interleaving the transmission resources for the plurality of pilots so that at least some of the pilots occupy transmission resources that do not appear on the rectangular grid in the delay-Doppler domain. In some embodiments, each additional pilot signal position may be interleaved from the n original positions on the rectangular grid. For example, in various embodiments, all even (or odd) pilot signals may be interleaved.

[0496] In some embodiments, the set of transmission resources occupied by any given pilot signal in the time-frequency domain corresponds to a grid of time instances uniformly distributed along the time axis and having a first step size and frequencies uniformly distributed along the frequency axis and having a second step size. It will be understood that the step size in the time-frequency domain is different from the frequency domain spacing of the pilot signal.

[0497] In some implementations, the set of transmission resources occupied by the pilot signal in the time-frequency domain corresponds to a grid comprising time instances that are unevenly distributed along the time axis.

[0498] In some implementations, the set of transmission resources occupied by at least one pilot signal in the time-frequency domain corresponds to a grid of frequencies that are unevenly distributed along the frequency axis.

[0499] In some implementations, a transmission resource set occupied by at least one pilot signal in the time-frequency domain does not overlap with another resource set in the time-frequency domain where the wireless communication device transmits user data.

[0500] In some implementations, transmitting operation 3308 includes transmitting a pilot signal to a given user equipment prior to transmitting data to the user equipment.

[0501] In some embodiments, the pilot signal may be generated by scrambling a base signal using a two-dimensional (2D) chirped sequence. In some embodiments, the pilot signal may be generated by cyclically shifting a root 2D Zadoff-Chu sequence by different amounts. The shifting may be performed in the time domain and / or the frequency domain.

[0502] In some embodiments, the transmission 3308 may be performed continuously from the transmitter to the user equipment regardless of whether there is data transmission from the transmitter to the UE. In some embodiments, the data may be precoded before transmission.

[0503] In some implementations, each pilot signal generated by a wireless device using method 3300 may occupy non-overlapping, discrete transmission resources.

[0504] In some embodiments, the wireless communication device includes a base station, and the method 3300 further includes generating at least two pilot signals occupying two non-overlapping transmission resource sets in the delay-Doppler domain. In some embodiments, the at least two pilot signals use non-overlapping delay domain resources. In some embodiments, the at least two pilot signals use non-overlapping Doppler domain resources.

[0505] In some embodiments, the wireless communication device comprises a user equipment, wherein the set of transmission resources is specified for the wireless communication device in an upper layer message.

[0506] Fig.343400, which includes a memory 3402 for storing instructions, a processor 3404, and a transmitter 3406. The transmitter 3406 is communicatively connected to the processor 3404 and the memory 3402. The memory 3402 stores instructions for the processor 3404 to generate a pilot signal according to the methods described herein (e.g., method 3300 and method 3500). The transmitter 3404 transmits the pilot signal on the wireless communication channel using the transmission resources designated for the transmission of the pilot signal.

[0507] Fig.35 A flow chart of an exemplary method 3500 for wireless communication is shown. The method 3500 includes the following operations: determining (3502) a maximum delay spread for a transmission channel, determining a maximum Doppler spread for the transmission channel, determining (3506) a plurality of pilot signals that can be sent using a two-dimensional transmission resource set based on at least the maximum delay spread and the maximum Doppler spread, allocating (3508) a transmission resource set from the two-dimensional resource set to a plurality of pilots, and sending (3510) the pilot signal on a wireless communication channel using the transmission resources. Various examples and options are disclosed in detail in Section 9 herein.

[0508] In some embodiments, operation 3506 may include determining a plurality of pilot signals based on one or more of the plurality of receivers to send the pilot signals to a plurality of transmission layers for transmission to the receivers, the plurality of receivers also sending the pilot signals and possibly interference from a pilot signal of another cell. As previously described, the target observation window may be determined in the time-frequency domain based on a desired resolution and observation time.

[0509] In some implementations, the pilot signals may be staggered. Fig.29 and Fig.30 Some examples are described and shown.Interleaving can be done by reallocating pilots from locations on one grid to locations along one of the dimensions (time or frequency) to maximize separation from non-interleaved pilots.

[0510] Fig.36 3600 is a block diagram of an example of a wireless communication device that can be used to implement some of the techniques disclosed in this patent document. Device 3600 can be used to implement method 3300 or 3500. Device 3600 includes a processor 3602, a memory 3604 that stores processor-executable instructions and data during operations performed by the processor. Device 3600 includes receiving and / or transmitting circuitry 3606, for example, including radio frequency operations for receiving or transmitting signals.

[0511] It will be appreciated that various techniques are disclosed for pilot encapsulation in an OTFS-based communication network.

[0512] The disclosed and other embodiments and the functional operations described herein may be implemented in digital electronic circuits, computer software, firmware or hardware (including the structures disclosed herein and their equivalent structures or a combination of one or more of them). The disclosed and other embodiments may 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 that are executed by a data processing device or control the operation of a data processing device. The computer-readable medium may be a machine-readable storage device, a machine-readable storage substrate, a memory device, a composition of matter that implements a machine-readable propagation signal, or a combination of one or more of them. The term "data processing device" includes all devices, equipment and machines for processing data, including programmable processors, computers, or multiprocessors or computers. In addition to hardware, the device may include code that creates an execution link for the computer program in question (e.g., code that constructs processor firmware), a protocol stack, a database management system, an operating system, or a combination of one or more of them. The propagated signal is an artificially generated signal, such as a machine-generated electrical, optical or electromagnetic signal, which is generated to encode information for sending to a suitable receiver device.

[0513] A computer program (also referred to as a program, software, software application, script, or code) can be written in any programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program does not necessarily correspond to a file in a file system. A program may be stored in a portion of a file that has other programs or data (e.g., one or more scripts stored in a markup language file), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., a file storing a portion of one or more modules, subroutines, or code). A computer program may be deployed to execute on one computer located at one location or on multiple computers distributed at multiple locations and interconnected by a communications network.

[0514] The processes and logic flows described herein may 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 may also be performed by, or the apparatus may be implemented as, special purpose logic circuitry, such as an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit).

[0515] Processors suitable for executing computer programs include, by way of example, one or more processors of general and special microprocessors and any type of digital computer. Generally, the processor will receive instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer are a processor for executing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to, from one or more large-capacity storage devices (e.g., magnetic disks, magneto-optical disks, optical disks) for storing data to receive data from the one or more large-capacity storage devices or to transfer data to the one or more large-capacity storage devices. However, the computer does not need to have these 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 such as EPROM, EEPROM and flash memory devices, magnetic disks such as built-in hard disks or removable disks, magneto-optical disks and CD ROM and DVD-ROM disks. Processors and memory can be supplemented by dedicated logic circuits or incorporated into dedicated logic circuits.

[0516] Although many details are included herein, these details should not be interpreted as limitations on the scope of the invention but as descriptions of features for specific embodiments. Some features described herein in the context of separate embodiments may also be implemented in combination in a single embodiment. On the contrary, each feature described in the context of a single embodiment may also be implemented individually in multiple embodiments or in any appropriate sub-combination. Moreover, although features may be described above as acting in some combinations and even initially claimed to be so, one or more features from the claimed combination may be removed from the combination in some cases and the claimed combination may be converted to a variation of a sub-combination or a sub-combination. Similarly, although operations are described in a specific order in the accompanying drawings, it should not be understood that these operations are required to be performed in the specific order shown or in sequence, or that all operations shown are performed to achieve the desired result.

[0517] Only some examples and implementations are described. Variations, modifications and enhancements of the described examples and implementations, as well as other implementations, may be made based on what is disclosed.

Claims

1. A wireless communication method implemented by a wireless communication device, comprising: receiving a plurality of pilot signals on a wireless communication channel, wherein a transmission resource set in the time-frequency domain is allocated to the plurality of pilot signals in the time-frequency domain based on a maximum delay spread determined for a transmission channel and a maximum Doppler spread determined for the transmission channel, wherein pilot signals of the plurality of pilot signals are packed within the transmission resource set using one of the following: (a) delay-Doppler pilot packing by arranging the pilot signals in a delay-Doppler plane to minimize leakage of the pilot signals between each other after experiencing a worst-case delay and Doppler shift of a channel; (b) time-frequency pilot packing by assigning a different grid to each pilot signal; or (c): a combination of (a) and (b), and wherein the plurality of pilot signals are transmitted over a wireless communication channel using transmission resources in a transmission resource set designated for pilot signal transmission using orthogonal time-frequency-space (OTFS) modulation, wherein each pilot signal in the plurality of pilot signals corresponds to a delta function in a delay-Doppler domain based on applying an inverse symplectic discrete Fourier transform to the plurality of pilot signals; processing the received plurality of pilot signals; and The wireless communication device is operated based on the received plurality of pilot signals.

2. The method according to claim 1, wherein: Processing the received plurality of pilot signals comprises: Converting the received plurality of pilot signals from a waveform domain to a time-frequency domain; and A symplectic Fourier transform is applied to the converted plurality of pilot signals, wherein the applying converts the converted plurality of pilot signals from a time-frequency domain to a delay-Doppler domain.

3. The method according to claim 1, wherein: The communication device includes a base station, and the receiving includes: A pilot signal is received by the base station from each active user equipment UE in the cell and at the edge of adjacent cells.

4. The method according to claim 3, wherein: Operating the wireless communication device comprises: Channel estimation is performed by the base station based on the pilot signal received from each active UE to demodulate uplink transmissions.

5. The method according to claim 3, wherein: Operating the wireless communication device comprises: The pilot information history of each active UE is collected from the pilot signal received from each active UE.

6. The method according to claim 5, wherein: Operating the wireless communication device further comprises: Calculating, by the base station, a precoder for the specific UE based on the collected pilot information history of the specific UE among the active UEs; and Downlink transmissions to the specific UE are precoded using the calculated precoder.

7. The method according to claim 6, wherein: The base station does not send a demodulation pilot signal to the specific UE on a spatial layer corresponding to a precoded downlink transmission.

8. The method according to claim 5, wherein: Operating the wireless communication device further comprises: Channel estimation is performed by the base station based on the collected pilot information history of each of the active UEs to demodulate uplink transmissions.

9. The method according to claim 1, wherein: The wireless communication device includes a user equipment UE, and the receiving includes: The plurality of pilot signals are received by the UE from a base station.

10. The method according to claim 9, wherein: Operating the wireless communication device comprises: Channel estimation is performed by the UE based on the received plurality of pilot signals to demodulate a non-precoded transmission from the base station.

11. The method according to claim 9, wherein: Operating the wireless communication device comprises: The UE measures and observes a time difference of arrival (OTDOA) based on the received multiple pilot signals.

12. The method according to claim 9, wherein: Operating the wireless communication device comprises: A pilot information history among the plurality of received pilot signals is collected by the UE.

13. The method according to claim 12, wherein: Operating the wireless communication device further comprises: performing, by the UE, channel estimation based on the pilot information history collected for the base station to demodulate a non-precoded transmission from the base station, or A time difference of arrival (OTDOA) is observed by the base station based on historical measurements of pilot information collected for the base station.

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