Method for sending or receiving symbols via an orthogonal time-frequency space communication channel with Doppler spreading and the method-implementing transmitter or receiver.

Abstract

A method (100) for transmitting a binary data sequence over a Doppler-spread OTFS (Orthogonal Time Frequency Space) communication channel, comprising: - receiving (102) a binary data sequence (b) to be transmitted, - encoding (104) the binary data sequence (b) in a channel encoder which generates a coded bit stream (b c ) outputs, - mapping (108) the bit stream (b c ) to data symbols (x d ), - Superimposing (118) pilot signals (x sp ) via the data signals (x d ), to receive a transmission signal (x), - Modulating (120) the transmission signal (x), and - transmitting (122) the modulated signal over the OTFS communication channel, the method further comprising, prior to the overlaying (118): - receiving (110) information concerning OTFS system parameters, including one or more of the number of delay ranges (M), the number of Doppler ranges (N), the carrier frequency (f c ), and the subcarrier spacing (Δf), - receiving (112) information concerning the OTFS communication channel, including one or more of the channel correlation matrix (R hh ), the channel length (L), the BEM order (Q), and the Gaussian noise variance (σ 2 ), - determining (114) a power allocation ratio (α*) of the pilot signals to be used for the superposition (118) exclusively on the basis of the received system parameters and the received channel information, and - Providing (116) the determined power allocation ratio (α*) of the pilot signals to the superposition step (118).

Description

FIELD OF INVENTION

[0001] The present invention relates to a method for transmitting and receiving symbols over a Doppler-spreading communication channel in the orthogonal time-frequency space (OTFS), and to transmitters and receivers implementing the method. SPELLINGS

[0002] In this specification, bold symbols represent vectors or matrices. Scalar values ​​are represented in this specification by lowercase italic letters, such as x. The superscript letters T, H, and † denotes the transpose, the complex conjugate transpose, and the pseudo-inverse of a vector or matrix, respectively. diag {a} is a diagonal matrix with vector a on its diagonal, while diag {A} is a vector whose elements lie on the diagonal of matrix A. ⊗ is the Kronecker product. BACKGROUND

[0003] Sixth generation (6G) and beyond wireless communications are expected to serve a large number of highly mobile users, e.g., vehicles, subways, highways, trains, drones, LEO (Low Earth Orbit) satellites, etc.

[0004] The preceding fourth and fifth generation (5G) of wireless communications uses orthogonal frequency division multiplexing (OFDM), which offers high spectral efficiency and high robustness against channels with frequency-selective fading, and also enables the use of low-complexity equalizers. However, due to velocity-dependent Doppler shifts or spreads and rapidly varying multipath reception, highly mobile communications suffer from severe time and frequency dispersion. Time and frequency dispersion each lead to signal fading at the receiver, which is therefore also referred to as doubly selective channel fading. Doubly selective channel fading significantly impairs the performance of OFDM communications.

[0005] As an alternative to OFDM, OTFS modulation is considered a promising modulation technique for sixth generation (6G) wireless communications, as it provides a solution for handling channels with dual selective fading.

[0006] OTFS modulation is a 2D modulation technique in which QAM information symbols are multiplexed over carrier waveforms corresponding to localized pulses in a signal representation known as a delay-Doppler representation. The OTFS waveforms are spread in both time and frequency and remain approximately orthogonal to each other under general delay-Doppler channel distortion. In theory, OTFS combines the reliability and robustness of spread-spectrum transmission with the high spectral efficiency and low complexity of narrowband transmission.

[0007] The OTFS waveforms couple to the radio channel in a way that directly maps the underlying physics, providing a high-resolution delay Doppler radar image of the individual reflectors. This transforms the time- and frequency-selective channel into an invariant, separately manageable, and orthogonal interaction in which all received symbols experience the same localized distortion and all delay Doppler diversity paths are coherently combined.

[0008] This makes OTFS ideal for radio communication between transmitters and receivers that move at high speed relative to each other, e.g. receivers or transmitters in high-speed trains, cars and even airplanes.

[0009] Fig.Figure 1 shows a block diagram of a general OTFS transmission system. A transmitter 200 includes a first transmitter-side transformation unit 202 and a second transmitter-side transformation unit 204. Serial binary data is input to a signal mapper (not shown in the figure), which outputs a two-dimensional sequence of information symbols x[k, l] in which the QAM symbols are arranged along the delay axis and the Doppler axis of the delay-Doppler domain. The information symbols include data symbols, pilot symbols, and guard symbols surrounding the pilot symbols. The two-dimensional sequence of information symbols x[k, l] is input to the first transmitter-side transformation unit 202 and subjected to an inverse finite symplectic Fourier transform (iSFFT), which generates a matrix X[n, m] representing the two-dimensional sequence of information symbols x[k, l] in the time-frequency domain.Since the transmitter transmits in the time domain, a further transformation is required in the second transmitter-side transformation unit 204, which generates the signal s[t] in the time domain, e.g., a Heisenberg transformation. The signal s[t] is then transmitted over the communication channel via an antenna 206.

[0010] In a realistic environment, the transmitted signal undergoes double selective fading with Doppler spread on its path from the transmitter through the communication channel to the receiver. The received signal is a superposition of a direct copy and a multitude of reflected copies of the transmitted signal, with each copy delayed by a path delay that depends on the length of the signal's path delay and frequency shifted by the Doppler shift that depends on the differential velocity between the transmitter, reflector, and receiver. Each of the signal copies is weighted according to its respective path delay and differential velocity. Typical Doppler shifts are on the order of 10 Hz - 1 kHz, although larger values ​​can occur in scenarios with extremely high mobility (e.g., high-speed trains) and / or high carrier frequency.Since realistic environments are likely to contain multiple reflectors and / or moving reflectors, the received superimposed signal is spread over a frequency range rather than merely shifted in frequency. This signal deformation is therefore also referred to as Doppler spreading. In the following description, the realistic communication channel is also referred to as the near-realistic communication channel.

[0011] In Fig.1, the realistic communication channel is represented by the undisturbed radio waves emitted by the transmitting antenna 206 and the various disordered radio waves arriving at the receiving antenna 302 from different directions and at different distances from each other. The radio waves can reach the receiver's antenna directly or after one or more reflections from one or more stationary and / or moving objects, which can lead to a Doppler shift and different delays of the reflected radio waves.

[0012] The receiver 300 receives the received signal r[t] in the time domain, which is fed to a first receiver-side transformation unit 304, where it undergoes a Wigner transform to transform the received signal r[t] into a matrix Y[n, m] representing the received signal r[t] in the time-frequency domain. To enable signal detection in the delay-Doppler domain, the matrix Y[n, m] is then fed to a second receiver-side transformation unit 306, where it undergoes a Finite Symplectic Fourier Transform (SFFT), which outputs a two-dimensional sequence of information symbols y[k, l] in the delay-Doppler domain.The two-dimensional sequence of information symbols y[k, l] is fed to a channel estimation and equalization block 310, which performs a channel estimation CE and a signal detection SD and reconstructs the originally transmitted symbols, and finally fed to a signal demapper, which outputs the originally transmitted binary data (signal demapper not shown in the figure).

[0013] To enable channel estimation in the receiver, pilot signals, also called pilots, can be added in the transmitter. These pilot signals, which are known in advance to the receiver, are located at known positions within the two-dimensional sequence of information symbols that is ultimately transmitted. While the pilot signals enable channel estimation with high accuracy and a low signal-to-noise ratio (SNR), the pilot signals, which take the place of data symbols, contain no data and thus reduce the spectral efficiency of the system. In known OTFS receivers with CE-BEM channel estimation, the pilot overhead must increase with increasing maximum transmission delay and Doppler spread to achieve acceptable performance, which further reduces spectral efficiency.While many OTFS channels have a known maximum transmission delay and possibly also a known maximum Doppler spread, real-world systems are designed for even higher maximum delay and Doppler spread to provide some safety margin. This further reduces spectral efficiency in such realistic systems.

[0014] An improvement in spectral efficiency can be achieved by using superimposed pilot signals and utilizing the freed-up space for data symbols. Superimposed pilot signals use low-power pilot signals that are superimposed on the data symbols in the delay Doppler domain. In addition to good spectral efficiency, superimposed pilot signals enable faster adaptation to time-variant channels.

[0015] Fig. 2 shows an illustration of superimposed pilot signals. As shown in the left part of Fig. As can be seen in Figure 2, the pilot signals can be arranged in the entire plane of the two-dimensional sequence of information symbols arranged along the delay axis and the Doppler axis of the delay-Doppler domain, but with a much lower power. The pilot signals are represented by the regular checkerboard pattern, indicating that the pilot signals are known in advance to the receiver. The data are represented by the random pattern, indicating the variability of the transmitted data. The power distribution is indicated by the distance from the delay-Doppler plane. The right part of Fig. Figure 2 shows an example power allocation to pilot signals and data symbols. It is easy to see that the pilot signals have much lower power than the data.

[0016] The data symbols and the pilots superimposed on them are transformed into the OTFS signal vector, which is finally transmitted after further transformations.

[0017] In the following consideration of the transmitted signal, M and N represent the dimensions of the delay grid and the Doppler grid, respectively, in which the symbols are arranged. The transmitted complex OTFS vector x, which consists of both superimposed pilot signals and data symbols, is defined as x=[x[0,0],x[0,1],…,x[0,M−1],…,x[N−1,0],x[N−1,1],…,x[N−1,M−1]]T.

[0018] In realistic scenarios, the transmission power for data and pilot signal transmission is limited, i.e., data symbols and pilot signals share the total transmission power available to the transmitter. The transmitted complex OTFS vector x can be represented as a superimposed pilot signal vector x sp and a data vector x dare represented in the delay-Doppler domain, which are defined as follows xsp = [xsp[0,0], xsp[0,1], …, xsp[0,M−1], …, xsp[N−1,0], xsp[N−1,1], …, sp[N−1,M−1]]^T, and xd = [xd[0,0], xd[0,1], …, xd[0,M−1], …, xd[N−1,0], xd[N−1,1], …, xd[N−1,M−1]]^T.

[0019] Let P T be the total transmission power and let α (α ∈ (0, 1)) denote the allocation ratio of the pilot signal power. It follows that αP T and (1 - α)P T are used for the transmission of pilot signals and data symbols respectively. Consequently, the transmitted OTFS signal vector x can be expressed as x = αxsp + √(1−α)xd, Note: There seems to be a small error in the original formula in line 18 where it should be √(1 - α)xd instead of 1−αxd for the formula to be correct in the context of power allocation for signal transmission. The translation has been adjusted accordingly.where α is the measure of the power assigned to the pilot signal. If more power is used for pilot transmission, i.e., if α is large, generally better power for channel estimation can be expected. However, less power would remain for data transmission, which leads to a low signal-to-noise ratio (SNR) and thus low reliability. In contrast, pilot signals to which less power is assigned, i.e., α is small, would lead to poor channel estimation and signal estimation. Therefore, an optimal power distribution between data and pilot signals is of utmost importance to achieve high reliability.

[0020] OTFS poses special challenges to channel estimation and equalization in a receiver. Therefore, channel estimation in wireless communication has been improved by introducing iterative processes that use already detected data as pseudo-pilot signals.

[0021] Iterative channel estimation, signal detection, and data decoding for single-carrier systems were proposed, for example, by H. Kim and J.K. Tugnait in "Turbo equalization for doubly-selective fading channels using nonlinear Kalman filtering and basis expansion models," IEEE Trans. Wireless Commun, vol. 9, no. 6, pp. 2076-2087, 2010, and by A. Movahedian and M. McGuire in "Estimation of fastfading channels for Turbo receivers with high-order modulation," IEEE Trans. Veh. Technol. vol. 62, no. 2, pp. 667-678, 2013. However, such single-carrier methods are not applicable to OTFS.

[0022] Iterative OTFS receivers using superimposed pilot signals were proposed by HB Mishra, P. Singh, AK Prasad, and R. Budhiraja in "OTFS channel estimation and data detection designs with superimposed pilots," IEEE Trans. Wireless Commun., vol. 21, no. 4, pp. 2258-2274, 2022, and in "Iterative channel estimation and data detection in OTFS using superimposed pilots," in Proc. IEEE Int. Conf. Commun. (ICC) Workshops 2021, Montreal, QC, Canada, 2021, pp. 1-6 by the same authors.

[0023] W. Yuan, S. Li, Z. Wei, J. Yuan, and DWK Ng discussed a related idea in “Data-aided channel estimation for OTFS systems with a superimposed pilot and data transmission scheme,” IEEE Wireless Commun. Lett., vol. 10, no. 9, pp. 1954–1958, 2021.

[0024] However, these previous works are only suitable for unrealistic Doppler shift channels and cannot be used in realistic Doppler spread communication channels.

[0025] Two basic expansion modeling (BEM) OTFS receivers for realistic channels with Doppler spread were proposed by the present inventors in "Near-optimal BEM OTFS receiver with low pilot overhead for high-mobility communications," IEEE Trans. Commun., vol. 70, no. 5, pp. 3392-3406, 2022, and in "BEM OTFS receiver with superimposed pilots over channels with Doppler and delay spread," in Proc. IEEE Int. Conf. Commun. (ICC), Seoul, South Korea, 2022, pp. 1-6.

[0026] In the former receiver, pilot signals arranged along the points of a grid in the delay-Doppler domain are surrounded by guard symbols. The number of guard symbols in each direction of the Doppler dimension is twice as large as the number of basis functions of the BEM used for modeling the communication channel in the receiver, and in the delay dimension twice as large as the maximum time delay. The receiver performs an initial pilot-assisted channel estimation using a BEM of a first BEM order and using the pilot signals, followed by an initial estimation of data symbols using the initial channel estimation, and iteratively performs a data-assisted channel estimation using a BEM of a second BEM order and at least the received data signals until a termination criterion is met. The receiver described above is also the subject of the published patent application DE 10 2021 126 321 A1.

[0027] The latter receiver is based on Karhunen-Loeve basis expansion modeling (KL-BEM), and an initial KL-BEM is performed using only the superimposed pilot signals. Subsequently, the pilot signals are removed, and equalization is performed using a message-passing method with subsequent signal detection. The pilot signals, together with the detected signals as pseudo-pilot signals, are used iteratively to refine the channel estimation and equalization. The receiver described above is also the subject of published patent application DE 10 2022 106 409 A1.

[0028] However, channel coding, a very important component in any communication system, was not considered in the inventors' previous work. For example, turbo and convolutional coding were used in fourth-generation (4G) long-term evolution (LTE) networks, while low-density parity check (LDPC) and polar coding were used in fifth-generation (5G) new radio (NR) networks.

[0029] The practical challenges associated with Doppler-spread channels were discussed by H. Qu, G. Liu, L. Zhang, M.A. Imran, and S. Wen in "Low-dimensional subspace estimation of continuous Doppler-spread channel in OTFS systems," IEEE Trans. Commun, vol. 69, no. 7, pp. 4717-4731, 2021. In this work, a subspace-based OTFS receiver was developed, but it requires a large number of dedicated pilot signals, resulting in low spectral efficiency.

[0030] While each of the solutions presented in the previous work has its advantages in certain, sometimes unrealistic scenarios, it is still desirable to provide an improved method for sending symbols over an OTFS communication channel using Doppler spread spectrum that offers high spectral efficiency. DESCRIPTION OF THE INVENTION

[0031] This object is achieved by the method according to claim 1, the apparatus according to claim 4, the wireless communication device according to claim 6, and the computer program product according to claim 7. A corresponding computer-readable storage medium is specified in claim 8. Advantageous embodiments and further developments are specified in the respective dependent claims.

[0032] A first aspect of the present invention aims to optimize the superimposed pilot signal power ratio α on the transmitter side. The optimized pilot signal power ratio α can be used in a method described herein as an example for iterative channel estimation, signal detection, and data decoding on the receiver side. The second aspect provides an apparatus implementing the method of the first aspect.

[0033] Before discussing the methods and apparatus for implementing the method in detail, the general system model of an encoded OTFS system is presented.

[0034] Fig. Figure 3 shows a block diagram of an exemplary coded OTFS system. Let b be a bit stream encoded by channel encoder 302 at a code rate R, which represents the coded bit stream b c results. b cis first interleaved in the interleaver 304 and then mapped in the signal mapper 306 to data symbols x using phase shift keying (PSK) or quadrature amplitude modulation (QAM). d shown. Superimposed pilot signals x sp are used and added to each data symbol in the pilot signal adding unit 308. x a and x sp are column vectors of length MN, where M and N are the number of OTFS delay and Doppler ranges, respectively. α(α ∈ [0,1]) is defined as the pilot signal power allocation ratio. The transmitted OTFS signal is given in the delay-Doppler domain by x=αxsp+1−αxd

[0035] After passing through the OTFS modulator 310, the signal is transmitted over the doubly selectively fading channel with Doppler spread, and the received signal is fed to the OTFS demodulator 404. The demodulated signal is fed to a channel estimator 406, whose output is used in a signal detector 408 to detect the transmitted symbols. The detected symbols are fed to the signal de-mapper 410, whose output is fed to the deinterleaver 412. The deinterleaved symbols are fed to the channel decoder 414, which then outputs the transmitted binary sequence b.

[0036] The received OTFS signal y in the delay Doppler domain output by the demodulator 404 is expressed as y=(FN⊗IM)Ht(FNH⊗IM)(αxsp+1−αxd)+w where F N the N-point discrete Fourier transform (DFT) matrix, I Mthe M × M identity matrix, w the vector of additive white Gaussian noise (AWGN) with a noise variance σw2 and H t is the MN × MN time-varying channel matrix in the time domain, which is defined as follows, Ht=[h[0,0]0⋯0h[0,L]h[0,L−1]⋯h[0,1]h[1,1]h[1,0]0⋯0h[1,L]⋯h[1,2]⋮⋱⋱⋱⋱⋱⋱⋮h[L,L ]h[L,L−1]⋯h[L,1]h[L,0]0⋯0⋮⋱⋱⋱⋱⋱⋱⋮0⋯0h[MN−1,L]h[MN−1,L−1]⋯h[MN−1,1]h[MN−1,0]] where h[t, l] denotes the channel gain of the l-th path at the t-th time, with t = 0, 1, ..., MN-1, and l=0,1, ..., L. L denotes the channel length. fmax=fcvc is defined as the maximum Doppler frequency, where f c is the carrier frequency, v is the vehicle speed, and c is the speed of light. Applying the Jakes model with U-shaped Doppler spectrum, the correlation function of the l-th path is given by J 0 (2πnf max T s ), where J 0(·) the Bessel function of the first kind of zeroth order and T s the sampling period.

[0037] By applying base expansion modeling (BEM) to model H t y can be formulated as y=∑q=0Q(FN⊗Im)diag{bq}FMNHdiag{FMN×Lcq}FMN(FNH⊗IM)(αxsp+1−αxd)+w+z where Q denotes the BEM order, ie, the number of BEM basis functions, b q and c q the q-th BEM basis function and its corresponding BEM coefficients are, F MN is the MN-point DFT matrix, F MN×L the (L + 1) columns of F MN and z is the error added to the received signal by the BEM modeling.

[0038] As discussed by the present inventors in “Near-optimal BEM OTFS receiver with low pilot overhead for high-mobility communications,” IEEE Trans. Commun., vol. 70, no. 5, pp. 3392-3406, 2022, the modeling error can be expressed as AWGN with a mean of zero and a variance of σz2 The above equation is therefore equivalent to y=α∑q=0Q(FN⊗Im)diag{bq}FMNHdiag{FMN(FNH⊗IM)xsp}FMN×Lcq︸Asp,q+1 −α∑q=0Q(FN⊗IM)diag{bq}FMNHdiag{FMN(FNH⊗Im)xd}FMN×L︸Ad,acq+w+z.

[0039] It should be noted that different Doppler spectral shapes may be possible depending on the environment. A selection of exemplary Doppler spectra is shown in Figures 18 to 23. Fig. Figure 18 shows the basic form of Jakes' U-shaped Doppler spectrum, which can be assumed, for example, when observing outdoor environments with fixed reflectors. Fig.Figure 19 shows the basic shape of an asymmetric Jakes Doppler spectrum, which can be assumed, for example, in general outdoor environments. Fig. Figure 20 shows a Gaussian Doppler spectrum that can be assumed for reception with mobile handsets, for example, in indoor or outdoor areas. Fig. 21 shows a rounded Doppler spectrum, which can be assumed, for example, in indoor or outdoor areas with fixed stations and movable reflectors. Fig. 22 shows a flat Doppler spectrum, which can be assumed, for example, in an indoor environment with fixed reflectors, and Fig. Figure 23 shows a bell-shaped Doppler spectrum, which can be assumed, for example, in general indoor environments. For comparison, Fig. 24 an exemplary representation of a pure integer Doppler shift, which is often assumed in OTFS considerations for the sake of simplicity without taking into account the conditions found in real environments.

[0040] To give a more concrete example, Fig. 25 a) a realistic Doppler spectrum for two vehicles moving in the same direction. The Doppler spectrum is similar to that shown in Fig. 23 is quite similar to the bell-shaped Doppler spectrum. Fig. 25 b) shows a realistic Doppler spectrum for two vehicles moving in opposite directions. Here, the Doppler spectrum is similar to the asymmetric U-shaped Jakes Doppler spectrum from Fig. 19 very similar.

[0041] It should also be noted that the BEM order Q required for satisfactory communication performance also varies with the type of Doppler spectrum assumed for a particular environment. Fig. Figure 26 shows an example graph illustrating this relationship. The bar marked (i) represents the BEM order for the Fig.24, while the bar labeled (ii) represents the BEM order for the Jakesian, asymmetric Jakesian, bell-shaped, flat, rounded, and fractional Doppler shifts, and the bar labeled (iii) represents the BEM order for the Gaussian Doppler shift. Note that the length of the bars is not to scale; the equations next to each bar provide more precise orders of magnitude.

[0042] The value of the BEM order Q has a significant influence on the optimal power allocation ratio α of the superimposed pilot signals, which requires appropriate optimization. Fig.Figure 27 shows the influence of an assumed Doppler spectrum on the power allocation ratio α of the superimposed pilot signals. The graph shows the signal-to-noise ratio (SNR) versus the power allocation ratio α of the superimposed pilot signals for three scenarios: 1) assuming an integer Doppler shift, represented by the circles, 2) assuming a Doppler spread with a Jakes, asymmetric Jakes, bell-shaped, flat or rounded shape or with a fractional Doppler shift, 3) Assuming a Doppler spread with a Gaussian shape.

[0043] It is easy to see that the optimal value of the power allocation ratio α of the superimposed pilot signals, i.e. the one that leads to the best SNR, varies depending on the scenario.

[0044] The following table shows the influence of other parameters, here: M, N, L, Q, σ 2 on the power allocation ratio α* of the superimposed pilot signals. A change in the value of a respective system parameter in the direction of the arrow leads to a change in the optimal power allocation ratio α* of the superimposed pilot signals in the direction indicated by the arrow in the same column. Changes in the system parameter values ​​in the opposite direction lead to a change in the optimal power allocation ratio α* of the superimposed pilot signals in the opposite direction. System parameters M ↗ N ↗ Q ↗ L ↗ s 2 ↘ α* ↘ ↘ ↗ ↗ ↗

[0045] Thus, according to a first aspect of the present invention, a method for transmitting a binary data sequence over an OTFS communication channel subject to Doppler spread is presented. The method includes, among other things, optimizing the power allocation ratio of the superimposed pilot signals. To avoid the need for end-to-end simulations or experiments, which are computationally intensive, cause undesirable latency, and / or consume channel resources, thus reducing the spectral efficiency of the communication system, the present invention specifically proposes a method for optimizing the power allocation ratio of the superimposed pilot signals that relies exclusively on information readily available at the transmitter.

[0046] As already mentioned, the transmitted OTFS signal in the delay Doppler domain is given by x=αxsp+1−αxd

[0047] The data signals and the superimposed pilot signals in the OTFS system are in matrices A d or A sp arranged. If you A sp = [A sp,0 , A sp,1 ,..., A sp,Q ], A d = [A d,0 , A d,1 ,..., A d,Q ] and c=[c0T,c1T,…,cQT]T defined, the above equation for y can also be written as y=αAspc+1−αAdc+w+z︸Interference+Noise+Modeling error.

[0048] By considering the data as interference, a first channel estimate can be made. 0 by using the matrix A representing superimposed pilot signals sp Accordingly, the received data signal is given by yd=y−αAspc^0=αAspc+1−αAdc+w+z−αAspc^0=αAsp(c−c^0)+1−αAd(c−c^0)+1−αAdc^0+w+z=1−αAdc^0︸Desired signal+(αAsp+1−αAd)(c−c^0)︸A︸Estimation error+Noise+Modelling error+w+z.

[0049] The SINR is therefore defined as SINR(α)=E{(1−α)(c^0)HAdHAdc^0}E{(c−c^0)HAHA(c−c^0)+wHw+zHz}

[0050] Denote SINR N and SINR D as the numerator or denominator of the above equation.

[0051] SINR N is given by SINRN=E{Trace{((1−α)AdHAdc^0(c^0)H}}=E{Trace{((1−α)AdHAd(c^0(c^0)H+ccH)}}=Trace{(1−α)E{AdHAd(c^0(c^0)H+ccH)}}=Trace{(1−α)E{AdHAd((AspHAsp )−1σw2+σz2+1−αα+ccH)}}=(1−α)Trace{E{AdHAd(AspHAsp)−1}}︸qσw2+σz2+1−αα+ (1−α)Trace{E{AdHAdccH}}=(1−α)q(σw2+σz2+1−α)α+(1−α)Trace{E{AdHAdccH}}. Let h be the vector of length MN(L + 1) representing the impulse response of the time-varying channel. The true BEM coefficient c is accordingly c = Dh, with D = (B ⊗ I L+1 ) † and the BEM basis functions B = [b 0 , b 1 , ... , b Q ]. Consequently, Trace{E{AdHAdccH}} can also be expressed as Trace{E{AdHAdccH}}=Trace{E{AdHAdDhhHDhH}}=Trace{E{DHAdHAdDhhH}}=Trace{E{DHAdHAdDhhH}}=Trace{E{DHAdHAd}E{hhH}}=Trace{E{DHAdHAdD}Rhh}=Trace{E{AdHAd}DRhhDH}≈Trace{Rhh}

[0052] If one has p = Trace{R hh}, SINR N finally be expressed as SINRN=(1−α)[q(σw2+σz2+1−α)+pα]α

[0053] SINR D is given by SINRD=E{Trace{AHA(c−c^0)(c−c0)H}}+MN(σw2+σz2)

[0054] According to the work of the present inventors in “Near-optimal BEM OTFS receiver with low pilot overhead for high-mobility communications,” IEEE Trans. Commun., vol. 70, no. 5, pp. 3392-3406, 2022, the BEM coefficient estimation error by using superimposed pilot signals can be given as follows: c˜0(c˜0)H=(c−c^0)(c−c^0)H=(AspHAsp)−1σw2+σw2+1−αα.

[0055] Consequently, SINR Dalso be expressed as SINDD=E{Trace{AHA(AspHAsp)−1σw2+σz2+1−αα}}︸K+MN(σw2+σz2). K cann wie folgt berechten werden K=E{Trace{(αAspHAsp+(1−α)AdHAd)(AspHAsp)−1σw2+σz2+1−αα}}=E{Trace{(1−α)AdHAd(AspHAsp)−1σw2+σz2+1−αα}}+(L+1)(Q+1)ασw2+σz2+1−αα=(1−α)(σw2+σz2+1−α)αTrace{E{AdHAd(AspHAsp)−1}}+(L+1)(Q+1)(σw2+σz2+1−α)=(1−α)(σw2+σz2+1−α)q+(L+1)(Q+1)(σw2+σz2+1−α)α where q=Trace{E{AdHAd(AspHAsp)−1}}.

[0056] SINR D can be finally ausgedrückt werden als SINRD=(1−α)(σw2+σz2+1−α)q+(L+1)(Q+1)(σw2+σz2+1−α)α+MNα(σw2+σz2)α=(σw2+σz2+1−α)((1−α)q+α(L+1)(Q+1))+MNα(σw2+σz2)α

[0057] Demnach ist SINR gegeben durch SINR(α)=(1−α)[q(σw2+σz2+1−α)+pα](σw2+σz2+1−α)((1−α)q+α(L+1)(Q+1))+MNα(σw2+σz2)α=(q−p)α2+(p−2q−q(σw2+σz2))α+q(σw2+σz2+1)(σw2+σz2+1−α)((1−α)q+α(L+1)(Q+1))+MNα(σw2+σz2)

[0058] Unter der Annahme, dass der volle Rang von AdHAd and AspHAsp achieved by appropriate BEM modeling, q can be defined as the full rank of E{AdHAd(AspHAsp)−1} and can be approximated as (L + 1)(Q + 1).

[0059] The SINR derived in this way is a function of the channel correlation matrix in the time domain R hhand can be used with various types of channel models, including the realistic Doppler-spread channel discussed by the present inventors in “Near-optimal BEM OTFS receiver with low pilot overhead for high-mobility communications,” IEEE Trans. Commun., vol. 70, no. 5, pp. 3392-3406, 2022 and in “BEM OTFS receiver with superimposed pilots over channels with Doppler and delay spread,” Proc. IEEE Int. Conf. Commun. (ICC), Seoul, South Korea, 2022, pp. 1-6, and also by H. Qu, G. Liu, L. Zhang, M.A. Imran, and S. Wen in “Low-dimensional subspace estimation of continuous Doppler-spread channel in OTFS systems,” IEEE Trans. Commun., vol. 69, no. 7, pp. 4717-4731, 2021, and also including the unrealistic Doppler shift channel discussed by HB Mishra, P. Singh, AK Prasad, and R. Budhiraja in “OTFS channel estimation and data detection designs with superimposed pilots,” IEEE Trans. Wireless Commun., vol.21, no. 4, pp. 2258-2274, 2022, and in “Iterative channel estimation and data detection in OTFS using superimposed pilots,” Proc. IEEE Int. Conf. Commun. (ICC) Workshops 2021, Montreal, QC, Canada, 2021, pp. 1-6, as well as by W. Yuan, S. Li, Z. Wei, J. Yuan, and DWK Ng in “Data-aided channel estimation for OTFS systems with a superimposed pilot and data transmission scheme,” IEEE Wireless Commun. Lett., vol. 10, no. 9, pp. 19541958, 2021, is discussed. In contrast to the approach presented above, the SINR derivation in existing works, e.g., by HB Mishra, P. Singh, AK Prasad, and R. Budhiraja in "OTFS channel estimation and data detection designs with superimposed pilots," IEEE Trans. Wireless Commun.", vol. 21, no. 4, pp. 2258-2274, 2022, is limited to unrealistic channels with Doppler shift.

[0060] The channel correlation matrix in the time domain R hhfor a channel path can be determined using previous channel estimates that may be available at the transmitter, e.g., a base station (BS) and / or the respective user equipment (UE). This is possible, among other things, because R hh or the second-order statistics of the channel compared to the vector ĥ j the channel impulse response of length MN for the j-th transmission frame changes more slowly over time than the channel itself.

[0061] An example block diagram of the input variables and the calculation is shown in Fig., in which the average is determined over a given number of previous "historical" channel correlation matrices for the jth frame. The number of historical channel correlation matrices forming a sliding window can be variable and can be changed dynamically as needed, e.g., if the channel suddenly changes significantly for external reasons. Of course, other methods for determining R hh be used.

[0062] Also in Fig. illustrated is the use of prior knowledge about the second-order statistics of the channel for resource allocation, improving channel estimation, etc., here illustrated by its use to determine the BEM order Q.

[0063] The power allocation ratio α of the pilot signals can be optimized by maximizing the SINR using the equation determined previously, i.e., α⋆=maxαSINR(α).

[0064] The optimal α* is obtained by solving the following function, i.e., dSINR(a)dα=0 where dSINR(a)dα=0 represents the first derivative of SINR(α) with respect to α.

[0065] Thus, the optimal power allocation ratio α* of the pilot signals can be determined on the transmitter side, which significantly saves resources, e.g., time, bandwidth, power, computations, etc., for end-to-end experiments or simulations.

[0066] Fig. Figure 4 shows a schematic representation of the inputs and outputs of the pilot signal adding unit 308, which carries out the method for optimizing the power allocation ratio of the pilot signals on the transmitter side according to the first aspect of the present invention. Information about the OTFS system parameters, ie, the number M of delay bands, the number N of Doppler bands, the carrier frequency f cand the subcarrier spacing Δf, and over the channel required, ie, the channel correlation matrix R hh , the channel length L, the BEM order Q, and the Gaussian noise variance σ 2 . L and Q refer to the relative velocity v between transmitter and receiver, f cand Δf. At least some of the information is also required for channel estimation and is, in most cases, available to the transmitter from a receiver located at the same location as the transmitter in bidirectional communication. As can be seen from the SINR derivation presented above, the derived SINR is approximate and does not depend on pilot signals and data symbols. Therefore, information about random pilot signals and data symbols, which are processed anyway in the pilot signal adding unit 308 of the transmitter, is optional for optimizing the power allocation ratio of the superimposed pilot signals. Nevertheless, the use of information about the pilot signals and data symbols can help to obtain a more accurate SINR.

[0067] If there are no significant changes in channel correlation (Doppler spectrum), channel length, velocity, and noise variance, there is generally no need to re-optimize α.

[0068] According to the first aspect of the present invention, a method for transmitting a binary data sequence over a Doppler-spread OTFS communication channel as described in Fig. 5, the reception of a binary data sequence b to be transmitted in step 102, the coding of the binary data sequence b in a channel encoder in step 104, which results in a coded bit stream b c and the mapping of the bit stream b c on data symbols x d In step 118, the data signals x d Pilot signals x spsuperimposed, resulting in a transmission signal x, which is OTFS-modulated in step 120 and transmitted over the OTFS communication channel in step 122. Before the superimposing step 118, the method includes receiving, in step 110, information about OTFS system parameters, including one or more of a number of delay ranges M, a number of Doppler ranges N, a carrier frequency f c , and a subcarrier spacing Δf. Furthermore, in step 112, information about the OTFS communication channel is received, including one or more of the elements channel correlation matrix R hh , channel length L, BEM order Q, and the Gaussian noise variance σ 2The information received in steps 110 and 112 is used in step 114 to determine a power allocation ratio α* of the pilot signal to be used for the superimposition in step 118, wherein the determination is based exclusively on the received system parameters and the received channel information as input. Determining the power allocation ratio of the superimposed pilot signal particularly includes maximizing the SINR, which depends solely on the received system parameters and the received channel information. The power allocation ratio α* of the pilot signal thus determined is fed to the superimposition step 118.

[0069] Steps 110 to 116 may be executed conditionally, e.g., only when changes in the information related to the channel information exceed corresponding predetermined values.

[0070] The channel encoder may be configured to output a forward error corrected bitstream, e.g., in accordance with turbo coding or low-density parity check (LDPC) coding.

[0071] In one or more embodiments, the method further comprises, before mapping the binary data sequence b to the data symbols x d in step 108, a step 106 of interleaving the binary data sequence b or the coded bit stream b c .

[0072] In one or more embodiments of the method, receiving OTFS channel information in step 112 includes performing a channel estimation for a signal received by a receiver 400 co-located with a transmitter 300 executing the method 100 to determine one or more of the OTFS channel information elements and / or to determine the SINR of the channel.

[0073] The optimization of the power allocation ratio of the superimposed pilot signal used for transmission as described above makes it possible to achieve a high convergence speed in a receiver not belonging to the present invention, as will be described below.

[0074] The invention can be used in a method not belonging to the present invention for receiving a binary data sequence transmitted over a Doppler-spread OTFS communication channel. The method comprises iterative channel estimation, signal detection, and data decoding, which are performed in two stages.

[0075] In a first, initial stage, after demodulation of the received OTFS signal (step 202), the channel is estimated (step 204) using only the pilot signals, e.g., the superimposed pilot signals whose power allocation ratio has been optimized according to the first aspect of the invention. In the case of superimposed pilot signals, the data symbols are treated as interference in the first stage.

[0076] Furthermore, in the first stage, signal detection is performed on the demodulated signal (step 206) using the results of the first channel estimation. The demodulated signal is then subjected to de-mapping (step 208), resulting in an initially received binary data sequence from which the binary data is reconstructed (step 212) using the forward error correction added to the binary data sequence at the transmitter. The reconstruction, which may include appropriate channel decoding, results in an initial reconstructed binary data set.

[0077] Next, values ​​related to probabilities or similarities are determined for the reconstructed binary data set, indicating the extent to which the reconstructed binary data correctly corresponds to the respective signals mapped in the transmitter (step 214). These values, which relate to probabilities or similarities, include, for example, log-likelihood ratios (LLR), mean and corresponding variance of the reconstructed data symbols, or similar. This determination step marks the beginning of a second, iterative phase.

[0078] As long as a termination criterion is not met ("n" branch of step 216), the reconstructed binary data and / or the associated probabilities or similarity values ​​are returned to the remapping step (step 208') (step 220), and a receiver-side mapping of the reconstructed binary data and / or the associated probabilities or similarity values ​​is performed in accordance with a mapping applied to the data on the transmitter side (step 222), and the receiver-side mapped data is fed to the signal detection step (step 206') and the channel estimation step (step 204'). The fed-back information is used as additional input for the respective method steps, which are iteratively repeated until the termination criterion is met.

[0079] If the termination criterion is met ("j" branch of step 216), the reconstructed binary data set is output (step 224). The termination criteria include, among other things, a predetermined number of iterations, one or more probabilities or similarity values ​​exceeding respective predetermined values, and / or a difference between one or more probabilities or similarity values ​​determined in two consecutive iterations that is less than a respective predetermined value.

[0080] The a posteriori LLRs determined based on the data output by the channel decoder can be fed back to reconstruct the a posteriori mean and variance of the data symbols, which are then used to refine channel estimation and signal detection. The respective extrinsic LLRs from the channel decoder are used as a priori LLR input for the demapter in the corresponding iterations.

[0081] A deinterleaving step (step 210, step 210') may be provided between the demapping step (step 208, step 208') and the reconstruction step (step 212, step 212'). In this case, a corresponding interleaving step (step 218') is provided before the reconstructed binary data and / or the associated probabilities or similarity-related values ​​are returned to the demapping step (step 208') (step 220) and the receiver-side mapping of the reconstructed binary data and / or the associated probabilities or similarity-related values ​​is performed (step 222).

[0082] A flowchart of the various steps of the method for receiving a binary data sequence with forward error correction and pilot signals added on the sender side, which are transmitted over an OTFS communication channel subject to Doppler spread is shown in Fig. FIG. 1, where the various steps are indicated in parentheses in the foregoing description. The dotted lines show the initially demodulated signal that is fed to the iteration stage. Dashed lines indicate optional steps.

[0083] In the following section, examples of channel estimation, signal detection, signal backmapping or signal mapping will be described in more detail. 1 Channel estimation:

[0084] Both initial and iterative channel estimation are described, using superimposed pilot signals and feedback averages of data estimates reconstructed from a posteriori LLRs of the channel decoder 1.1 Initial channel estimation:

[0085] By applying the optimized pilot signal allocation ratio α* to the superimposed pilot signals and treating the data as interference, the received OTFS signal is expressed as y=α⋆Aspc+1−α⋆Adc+w+z︸Interference+Noise+Modeling error.

[0086] Thus, the BEM coefficient c can be initially estimated by using superimposed pilot signals, c^0=Asp†yα⋆

[0087] The superscript 0 indicates that this is the initial channel estimate. 1.2 Iterative channel estimation:

[0088] In addition to the superimposed pilot signals, the a priori information, ie the a priori mean value of the data symbols mprii, from channel decoding and mapping to refine the channel estimation. To avoid noise amplification, the performance of mprii in relation to the power allocated to the data symbols for PSK modulation. In QAM modulation, the power of mprii on the power of that symbol χ h from the QAM modulation alphabet KQAM normalized, whose symbol probability Ppos,xd[n]=χhi is the highest among all candidates in the QAM modulation alphabet.

[0089] The normalized mean of the data symbol estimate is called m¯prii According to the definitions of A given above sp , A d , and c can A^d,qi be formulated as A^d,qi=(FN⊗IM)diag{bq}FMNHdiag{FMN(FNH⊗IM)m¯prii}FMN×L and thus results A^di as A^di=[A^d,0,iA^d,1i,…,A^d,Qi]. Therefore, the BEM coefficient c can be refined as follows c^i=(α*Asp+1−α*A^di)y†. 2 Signal detection:

[0090] With the BEM coefficient estimation ĉ i the received data signal is now calculated as follows y^di=y−α⋆Aspc^i=1−α⋆Adc+α⋆Asp(c−c^i)︸ei+w+z, where e i is the error due to the channel estimation and is a Gaussian random vector with a mean of zero and a variance σe,i2 can be viewed. σe,i2 is expressed as σe,i2=TRACE{α*Asp(c−c^i)(c−c^i)HAspH}MN=TRACE{α*AspHAsp(c−c^i)(c−c^i)H}MN

[0091] As the inventors have shown in “Near-optimal BEM OTFS receiver with low pilot overhead for high-mobility communications,” IEEE Trans. Commun., vol. 70, no. 5, pp. 3392-3406, 2022, (c - ĉ i )(c - ĉ i ) H given by (c−c^i)(c−c^i)H={(AspHAsp)−1σw2+σz2+1−ααi=0((α⋆Asp+1−α⋆A^di)H(α⋆Asp+1−α⋆A^di))−1(σw2+σz2)i≥1.

[0092] For i = 0 σe,i2 further given by σe,02=Trace{α⋆AspHAsp(AspHAsp)−1σw2+σz2+1*−α⋆α⋆}MN=(L+1)(Q+1)(σw2+σz2+1*−α⋆)MN.

[0093] For i ≥ 1, σe,i2 expressed as σe,i2=Trace{α⋆Asp((α⋆Asp+1−α⋆A^di)H(α⋆Asp+1−α⋆A^di))−1(σw2+σz2)AspH}MN.

[0094] Setting the right side of the previous equation to β, we can σe,i2 be expressed as σe,i2={(L+1)+(Q+1)(σw2+σz2+1−α⋆)MNi=0βi≥1.

[0095] Assuming that A^di to its true value A d , β is close to zero. As defined above, A d c equivalent to Dx d . Therefore, y^di as a Gaussian random variable with a mean of 1−α*Dxd and a variance of σ2=(σe2+σz2) be considered, ie y^di=1−α*Dxd+e+w+z.

[0096] With the BEM coefficient estimation ĉ i an estimate of D is given by D^=∑q=0Q(FN⊗IM)diag{bq}FMNHdiag{FMN×Lc^qi}FMN(FNH⊗IM)

[0097] With G=1−α*D^ are the initial a posteriori mean and the initial a posteriori variance of the data x d given by vposi=(GH(σ2)−1G+diag{vprii−1}−1)−1 mposi=vposi(GH(σ2)−1y^di+diag{vprii−1}−1mprii−1), where vprii−1 and mprii−1 are the a priori mean and a posteriori variance of the data symbols obtained by using the a posteriori LLR of the channel decoder. The technical details can be found later in this section. The extrinsic mean and variance of the n-th (n = 0, 1, ... , MN - 1) data symbol are calculated by vext,ni=((vposi[n,n])−1−(vprii−1[n])−1)−1, mext,ni=vext,ni(mposi[n]vposi[n,n]−mprii−1[n]vprii−1[n]). 3 Remap:

[0098] The de-imager has two input variables: • the extrinsic mean mext,ni and the variance vext,ni of the data symbol from symbol recognition; • a priori LLRs of the coded bits LE,prii−1 the extrinsic LLRs LD,exti−1 of the channel decoder.

[0099] The a priori LLRs are used to calculate the a priori symbol probability of the n-th data symbol Ppri,xd[n]=xi expressed as Ppri,xd[n]=xi−1∝∏k=0log2K−1e−x[k]LE,prii−1[nlog2K+k] where χ is the symbol from a specific modulation alphabet K whose modulation order is K, and χ[k] denotes the k-th bit in χ The a posteriori symbol probability of the n-th data symbol ppos,xd[n]=xi is then calculated by ppos,xd[n]=xi∝Ppri,xd[n]=xi−1×e−|x−mext,ni|2vext,ni.

[0100] With the a posteriori symbol probability Ppos,xd[n]=xi the a posteriori LLR of the k-th bit of the n-th data symbol is given by LM,posi[nlog2K+k]=log∑x∈K,x[k]=0Ppos,xd[n]=xi∑x∈K,x[k]=1Ppos,xd[n]=x.

[0101] The corresponding extrinsic LLR is expressed as LE,exti=LE,posi−LE,pri−1, which is passed to the deinterleaver and the channel decoder. Note that in the initial phase i=0,LE,pri0 on OMN log2K×1 is set.

[0102] The channel encoders and decoders that can be used in the present invention and the method not belonging to the present invention can be of known type, ie convolutional coding, e.g. turbo coding, and LDPC coding can be applied with the proposed OTFS system.

[0103] With LD,exti and LD,posi be the extrinsic and a posteriori LLRs of the channel decoder. LD,exti is returned to the de-mapper as its a priori LLRs. LD,posi passes through the mapper to calculate the a posteriori mean and a posteriori variance of a data symbol, which are used as a priori information for channel estimation and signal detection. 4 Illustration:

[0104] With a priori LLRs, the a posteriori LLRs LD,posi of the channel decoder, the a priori probability of the n-th data symbol is given by PM,pri,Xd[n]=xi∝∏k=0log2K−1e−x[k]LD,posi[nlog2K+k]

[0105] Thus, the a priori mean and variance of the n-th data symbol for channel estimation and signal detection can be expressed as mprii[n]=∑χ∈APM,pri,x,d[n]=χiχ, vprii=∑χ∈APM,pri,x,d[n]=χi|χ|2−|mprii[n]|2.

[0106] Now mprii[n] back to channel estimation to improve its performance, and both mprii[n] as well as vprii are fed into the signal detection system. It should be noted that in the initial phase i=0,PM,pri,x,d[n]=χi with the same probability as 1 / K.

[0107] The iterative process for channel estimation, signal detection, and channel decoding described above is repeated until a termination criterion is met. Examples of termination criteria are: • The difference in the data estimate variance for two consecutive iterations is below a predefined threshold λ, i.e. |vprii−vprii−1|<λ; • A specified number of iterations I is reached.

[0108] Any of the above termination criteria is sufficient to terminate the iterations.

[0109] Fig.7 shows a block diagram of an OTFS system comprising a transmitter 300 according to the second aspect of the invention and a receiver 400 not belonging to the present invention. The transmitter 300 is configured to perform a method 100 for transmitting a binary data sequence over a Doppler-spread OTFS communication channel according to the first aspect of the present invention, including optimizing the power allocation ratio of the superimposed pilot signals. The receiver 400 is configured to perform a method 200 for receiving a binary data sequence with transmitter-added forward error correction and pilot signals transmitted over a Doppler-spread OTFS communication channel, including two-stage iterative channel estimation, signal detection, and data decoding.

[0110] The transmitter 300 according to the second aspect of the invention for use in an OTFS system comprises a channel encoder 302 configured to receive a binary data sequence b, a signal mapper 306 configured to receive an output signal from the channel encoder and to convert data signals x d to output, a pilot signal adding unit 308 which is arranged to output pilot signals x p to the data signals x d and output a signal to be transmitted x to an OTFS modulator 310, which is configured to apply an OTFS modulation to the signal to be transmitted x in order to transmit the modulated signal through one or more antennas 312 over an OTFS communication channel. The pilot signal adding unit 308 is further configured to optimize a power allocation ratio (α) of the pilot signals according to embodiments of the method 100 according to the first aspect of the invention.

[0111] The transmitter 300 may further include an interleaver 304 upstream of the signal mapper 306.

[0112] A receiver 400 for use in an OTFS system, not belonging to the present invention, includes an antenna 402 for receiving OTFS-modulated signals over a Doppler-spread OTFS communication channel and for providing the received signal to an OTFS demodulator 404. The OTFS demodulator 404 outputs a received signal y to a channel estimator 406. The channel estimator 406 further receives an uncorrupted copy of the superimposed pilot signals x pand outputs an estimate of the channel coefficients to a signal detector 408. The signal detector 408 is configured to detect transmitted signals in the received signal y and output detected signals to a signal de-mapping unit 410. The de-mapping units are fed to a channel decoder 414, which outputs a reconstructed version b' of the transmitted binary data sequence b. After initial processing of the received signal in the previously described processing chain, signals representing intermediate processing results are fed back to corresponding upstream processing blocks to refine the intermediate processing results and ultimately the output signal of the receiver 300 in an iterative stage.Specifically, the output signal of the channel decoder 414 is fed to a processing unit configured to determine, for the reconstructed version b' of the transmitted binary data sequence b, values ​​relating to probabilities or similarities that indicate the extent to which the reconstructed version b' of the transmitted binary data sequence b correctly corresponds to the respective transmitted data. The values ​​relating to probabilities or similarities are fed to the signal demapping unit 410 as a further input signal, and at least one of the values ​​relating to probabilities or similarities is fed to the signal detector 408 or the channel estimator 406 via a receiver-side signal mapping unit 418.

[0113] The output signal of the signal mapper 410 may be subtracted from the probabilities or similarity values ​​returned to the signal mapper 410.

[0114] A deinterleaver 412 may be arranged between the signal demapper 410 and the channel decoder 414, and an interleaver 416 may be configured to receive the output signal of the processing unit configured to determine probabilities or similarity-related values, wherein at least one of the probabilities or similarity-related values ​​output by the interleaver 416 is fed back to the deinterleaver 410 and, via the receiver-side signal demapper 418, to the signal detector 408 or the channel estimator 406.

[0115] The various functional blocks of the transmitter 300 according to the present invention and the receiver 400 not belonging to the present invention may be implemented by computer program instructions stored in non-volatile memory and executed by a microprocessor in conjunction with a random access memory. One or more of the functional blocks of the transmitter 300 or the receiver 400 may be implemented, at least in part, on dedicated hardware controlled by computer program instructions executed by the microprocessor.

[0116] Monte Carlo simulations were conducted to demonstrate the performance of the proposed OTFS system. The simulation settings are shown in Table I. Table I System parameters Value Carrier frequency (fc) 4 GHz Subcarrier spacing (Δf) 15 kHz Number of delay ranges (M) 128 Number of Doppler ranges (N) 16 Channel model 5G TDL-B Vehicle speed (v) 125 km / h Modulation scheme QPSK Channel coding LDPC coding with a coding rate of 1 / 2

[0117] The number of OTFS delay and Doppler ranges is set to M = 128 and N = 16. The carrier frequency and subcarrier spacing are set to f c = 4 GHz and Δf = 15 kHz. A 5G TDL B-channel model with a channel length of L = 5 and Jakes Doppler spectrum is used. The vehicle speed is 125 km / h, and the modulation scheme is quadrature PSK (QPSK). LDPC coding with a coding rate of 1 / 2 is used.

[0118] The Fig. 8 and Fig. 9 show the SINR and BER of the proposed OTFS system as a function of the power allocation ratio α of the superimposed pilot signals for EbN0 = 10 dB. The theoretical value of the optimal α is calculated as approximately α* = 0.2659 by using the function dSINR(a)dα=0 is solved with the expression for SINR(α) derived above. In the Fig. 8 and Fig.9 shows that α* = 0.2659 results in the highest SINR and the lowest BER, confirming the effectiveness of the algorithm described here to optimize the power allocation ratio for the superimposed pilot signals.

[0119] The Fig. 10 and Fig. Figure 11 shows the MSE of the channel estimation and the BER of the proposed OTFS system as a function of the number of iterations for EbN0 = 7.5 dB and EbN0 = 10 dB. The proposed OTFS system converges quickly within 2 iterations for both the MSE of the channel estimation and the BER, thanks to the optimization of the ratio of the superimposed pilot signals α described above.

[0120] Fig.Figure 12 shows the extrinsic information transfer (EXIT) diagrams and the trajectory path of the proposed OTFS system for EbN0 = 10 dB. The trajectory path consists of 2 steps, which means that 2 iterations are required for the proposed OTFS system. The convergence speed by analyzing the EXIT diagram in Fig. agrees with what is stated in the Fig. can be observed.

[0121] Fig.Figure 13 shows the BER of the proposed OTFS system compared to example existing systems that do not consider channel coding, e.g., as described by H. Qu, G. Liu, L. Zhang, M.A. Imran, and S. Wen in “Low-dimensional subspace estimation of continuous Doppler-spread channel in OTFS systems,” IEEE Trans. Commun., vol. 69, no. 7, pp. 4717-4731, 2021 (denoted as “LSQR” in the figure), as described by P. Singh, S. Tiwari, and R. Budhiraja in “Lowcomplexity LMMSE receiver design for practical-pulse-shaped MIMO-OTFS systems,” IEEE Trans. Commun., vol. 70, no. 12, pp. 8383-8399, 2022 (referred to as “LMMSE” in the figure), and as described by P. Raviteja, KT Phan, Y. Hong, and E. Viterbo in “Interference cancellation and iterative detection for orthogonal time frequency space modulation,” IEEE Trans. Wireless Commun., vol. 17, no. 10, pp. 65016515, 2018 (referred to as “MP” in the figure).

[0122] Perfect channel estimation is assumed for the comparison. Note that the MP equalization algorithm discussed by P. Raviteja, KT Phan, Y. Hong, and E. Viterbo in "Interference cancellation and iterative detection for orthogonal time frequency space modulation" was adopted in the present inventors' previous works "Near-optimal BEM OTFS receiver with low pilot overhead for high-mobility communications" and "BEM OTFS receiver with superimposed pilots over channels with Doppler and delay spread." It can be seen that the proposed OTFS system with channel coding significantly outperforms the example existing systems, and an SNR gain of up to 5 dB can be achieved. Note that perfect channel estimation is assumed for the benchmark.

[0123] In Fig.14 compares the BER of the proposed OTFS system with the example system using convolutional coding presented by H. Qu, G. Liu, L. Zhang, M.A. Imran, and S. Wen in "Low-dimensional subspace estimation of continuous Doppler-spread channel in OTFS systems." The proposed OTFS system performs slightly worse than the existing example system when EbN0 is below 5 dB. For EbN0 > 5 dB, the proposed OTFS system can achieve an EbN0 gain of up to 4 dB. Note that perfect channel estimation is assumed for the benchmark.

[0124] The Fig. 15 and Fig. 16 show the MSE of the channel estimation and the coded BER of the proposed OTFS system compared to that in Fig.14. For a fair comparison, identical power allocation ratios α = 10% for the pilot signals are chosen for both systems. The proposed OTFS system has no dedicated pilot signal overhead, i.e., λ = 0, while the existing example system requires a dedicated pilot signal overhead of λ = 10%. The proposed OTFS system performs worse than the existing example system at low EbN0 because the existing example system is supported by dedicated pilot signals and there is no interference between pilot signals and data. In contrast, the proposed OTFS system is based on superimposed pilot signals, and there is always interference between pilot signals and data.Due to data interference and large noise variance at low EbN0, channel estimation based on superimposed pilot signals cannot provide good channel and data estimation, so the subsequent data-based channel estimation cannot further refine the channel estimation. This situation is mitigated at medium to high EbN0. In particular, for EbN0 > 6 dB, the proposed OTFS system can achieve an EbN0 gain of 4 dB over the existing example system. Therefore, the proposed OTFS system not only provides improved spectral efficiency but also achieves higher reliability than the existing example system, especially at medium to high EbN0.

[0125] The method presented here and the device implementing this method advantageously utilizes a novel derivation and analytical expression for the SINR, which can be used, among other things, for practical OTFS communication channels subject to Doppler spread, as well as for less demanding Doppler-shifted channels. The new analytical SINR expression enables the determination of an optimized power allocation ratio for the superimposed pilot signals at the transmitter side using only information that is readily available at the transmitter side, i.e., without having to rely on end-to-end attempts or on information fed back to the transmitter via the communication channel or otherwise, which consumes additional resources and increases latency. The required information includes the OTFS system parameters and various channel information parameters, e.g.,the channel correlation matrix, the noise variance, etc. This saves time and resources, including energy, computations, and bandwidth on the communication channel, and enables dynamic adjustment of the power allocation ratio of the superimposed pilot signals when changes in the communication environment require it. Adjusting the power allocation ratio of the superimposed pilot signals depending on the type or shape of the Doppler spectrum encountered or expected in a particular application also enables the achievement of an optimal SNR. The two-stage iterative design of the receiver, whose designs apply and integrate the Turbo concept to an OTFS system, is low in complexity and offers fast convergence, thus reducing latency.The optimized pilot signal power allocation ratio further enhances the benefits already achieved by iterative channel estimation, signal detection, and data decoding, including receiver convergence speed, while maintaining the higher spectral efficiency of the superimposed pilot signals compared to dedicated pilot signals. The inclusion of channel decoding in the channel estimation iterations results in increased performance in terms of channel estimation MSE and BER, especially at medium to high EbN0.

[0126] According to a third aspect of the invention, a wireless communication device, e.g. a transmitter of a base station or a user equipment, comprises one or more microprocessors, volatile and non-volatile memory, and a wireless interface circuit configured to transmit electromagnetic signals via one or more antennas. The various elements are communicatively connected to one another via one or more data or signal lines or buses. The non-volatile memory stores computer program instructions which, when executed by the microprocessor, configure the wireless device to carry out methods according to the first aspect of the invention, as set out above.

[0127] The methods described above can be represented by computer program instructions. Accordingly, a computer program product comprises computer program instructions that, when executed by a microprocessor of a transmitter, cause the microprocessor to execute embodiments of methods according to the first aspect of the present invention and, accordingly, to control hardware components of the transmitter of an OTFS communication system according to the second or third aspect of the invention, as described above.

[0128] The computer program instructions may be retrievably stored or transmitted on a computer-readable medium or storage device. The medium or storage device may be physically embodied, e.g., in the form of a hard disk, a solid-state disk, a flash memory, or the like. However, the medium or storage device may also comprise a modulated electromagnetic, electrical, or optical signal that is received by the computer using a corresponding receiver and transmitted to and stored in a memory of the computer.

[0129] The methods proposed here and the apparatus configured to carry out the methods can be advantageously used, among other things, in all types of wireless OTFS communication systems. The proposed methods and the corresponding apparatus can be advantageously used in highly mobile devices such as vehicles, trains, aircraft, and the like. SHORT DESCRIPTION OF THE DRAWING

[0130] Aspects of the present invention are described in more detail with reference to the figures in the drawing. The drawing shows Fig. 1 a block diagram of a general OTFS transmission system, Fig. 2 an illustration of superimposed pilot signals, Fig. 3 a block diagram of an exemplary coded OTFS system, Fig. 4 is a schematic diagram of the input signals and the output signal of the pilot signal adding unit that performs the method for optimizing the power allocation ratio of the pilot signals on the transmitter side in accordance with the first aspect of the present invention, Fig. 5 is an exemplary flowchart of a method for transmitting a binary data sequence over a Doppler-spread OTFS communication channel according to the first aspect of the present invention, Fig. 6 is an exemplary flowchart of the various steps of the method not belonging to the present invention for receiving a binary data sequence with forward error correction added at the transmitter end and pilot signals transmitted over an OTFS communication channel subject to Doppler spread, Fig. 7 is a block diagram of an OTFS system with a transmitter according to the invention and a receiver not belonging to the present invention, Fig. 8 the SINR of the proposed OTFS system as a function of the power allocation ratio α of the superimposed pilot signals for EbN0 = 10 dB, Fig. 9 the BER of the proposed OTFS system as a function of the power allocation ratio α of the superimposed pilot signals for EbN0 = 10 dB, Fig.10 the MSE of the channel estimation of the proposed OTFS system as a function of the number of iterations for EbN0 = 7.5 dB and EbN0 = 10 dB, Fig. 11 the BER of the proposed OTFS system as a function of the number of iterations for EbN0 = 7.5 dB and EbN0 = 10 dB, Fig. 12 the Extrinsic Information Transfer (EXIT) diagrams and the trajectory path of the proposed OTFS system for EbN0 = 10 dB, Fig. 13 the BER of the proposed OTFS system compared to exemplary existing systems that do not consider channel coding, Fig. 14 a comparison of the BER of the proposed OTFS system with an exemplary existing system, Fig. 15 the MSE of the channel estimation of the proposed OTFS system compared to that in Fig. used exemplary existing system, Fig.16 the coded BER of the proposed OTFS system compared to that in Fig. used exemplary existing system, Fig. 17 an exemplary block diagram of a transmitter according to the invention, Fig. 18 - Fig. 23 different exemplary basic forms of Doppler spectra that can be used depending on an environment, Fig. 24 an example representation of the Doppler shift, Fig. 25 exemplary realistic Doppler spectra for different environments, Fig. 26 a schematic representation of the dependence of the required BEM order on different Doppler spectra, Fig. 27 a representation of the influence of an assumed Doppler spectrum on the optimal power allocation ratio α of the superimposed pilot signals α, and Fig.28 shows an example block diagram of the inputs for calculating second-order channel statistics and for resource allocation.

[0131] In the figures, identical or similar elements may be designated by the same reference designations. DESCRIPTION OF EMBODIMENTS

[0132] The Fig. 1 to 16 and 18 to 28 have already been described above and will not be discussed again.

[0133] Fig.17 shows an exemplary block diagram of a transmitter 300 according to embodiments of the second aspect of the present invention. The transmitter 300 includes a microprocessor 350, a volatile memory 352, a non-volatile memory 354, and a wireless interface circuit 356 configured to communicate with a receiver by transmitting electromagnetic signals via a plurality of antennas 312. The aforementioned elements are communicatively connected via one or more signal or data links or buses 358. The non-volatile memory 354 stores computer program instructions that, when executed by the microprocessor 350, cause the transmitter 300 to perform the method according to the first aspect of the present invention as presented herein. LIST OF REFERENCE SYMBOLS (PART OF THE DESCRIPTION) 100 transmission methods 102 binary data sequence received 104 encode binary data sequence 106 interleaved encoded data 108 Mapping 110 OTFS system information received 112 Receive channel information 114 Determine the performance allocation ratio 116 provide a specific performance allocation ratio 118 pilot signals superimposed 120 OTFS Modulators 122 Transfer 200 reception procedures 202 OTFS demodulation 204 Channel estimation 206 Signal detection 208 Re-mapping 210, 210' Unnesting 212, 212' Reconstruct data 214 Determining values ​​related to probabilities or similarities 216 Termination condition met? 218 Nesting 220 Feedback 222 receiver-side mapping 224 output reconstructed data 300 channels 302 channel encoders 304 Nesters 306 signal processors 308 pilot signal adder 310 OTFS Modulator 312 Antenna 350 microprocessor 352 volatile memory 354 non-volatile memory 356 wireless interface circuit 358 Signal / data connection / bus 400 recipients 402 Antenna 404 OTFS Demodulator 406 channel estimators 408 signal detectors 410 Signal Reconstructor 412 deinterleavers 414 channel decoder 416 nesters 418 signal processors

Claims

[1] A method (100) for transmitting a binary data sequence over an OTFS (Orthogonal Time Frequency Space) communication channel subject to Doppler spread, comprising: - receiving (102) a binary data sequence (b) to be transmitted, - encoding (104) the binary data sequence (b) in a channel encoder which generates a coded bit stream (b c ) outputs, - mapping (108) the bit stream (b c ) to data symbols (x d ), - Superimposing (118) pilot signals (x sp ) via the data signals (x d ), to receive a transmission signal (x), - Modulating (120) the transmission signal (x), and - transmitting (122) the modulated signal over the OTFS communication channel, the method further comprising, prior to the overlaying (118): - receiving (110) information concerning OTFS system parameters, including one or more of the number of delay ranges (M), the number of Doppler ranges (N), the carrier frequency (f c ), and the subcarrier spacing (Δf), - receiving (112) information concerning the OTFS communication channel, including one or more of the channel correlation matrix (R hh ), the channel length (L), the BEM order (Q), and the Gaussian noise variance (σ 2 ), - determining (114) a power allocation ratio (α*) of the pilot signals to be used for the superposition (118) exclusively on the basis of the received system parameters and the received channel information, and - Providing (116) the determined power allocation ratio (α*) of the pilot signals to the superposition step (118). [2] Method according to claim 1, before mapping (108) the bit stream (b c) to the data symbols (x d ) also includes: - interleaving (106) the binary data sequence (b) or the coded bit stream (b c ). [3] The method of claim 1 or 2, wherein receiving (112) information concerning the OTFS communication channel comprises performing a channel estimation based on a signal received by a receiver (400) arranged together with a transmitter (300) executing the method (100) to determine one or more of the channel information. [4] Transmitter (300) of an OTFS transmission system comprising a channel encoder (302) configured to receive a binary data sequence (b), a signal mapper (306) configured to receive an output signal of the channel encoder (302), a pilot signal adding unit (308) and an OTFS modulator (310) connected to one or more antennas (312), wherein the pilot signal adding unit (308) is further configured to optimize a power allocation ratio (α) of the pilot signal according to the method according to one or more of claims 1 to 3. [5] The transmitter (300) of claim 4, further comprising an interleaver (304) upstream of the signal mapper (306). [6] A wireless communication device (300) comprising one or more microprocessors (350), volatile (352) and non-volatile (354) memory, and a wireless interface circuit (356) configured to transmit electromagnetic signals via one or more antennas (312), wherein the non-volatile memory (354) stores computer program instructions which, when executed by the microprocessor (352), configure the wireless device (300) to carry out the methods of one or more of claims 1 to 3. [7] Computer program product comprising computer program instructions which, when executed by a microprocessor (352) of a wireless communication device configured as a transmitter (300), cause the microprocessor (352) to execute methods according to one or more of claims 1 to 3 and to control hardware components of the transmitter (300) of an OTFS communication system according to one or more of claims 4 or 5 accordingly. [8] A computer-readable medium or data carrier which retrievably transmits or stores the computer program product according to claim 7.

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