US-12627548-B2 - Receiver for and method of receiving symbols over time varying channels with doppler spread

US12627548B2US 12627548 B2US12627548 B2US 12627548B2US-12627548-B2

Abstract

A near-optimal Karhunen-Loeve basis expansion modeling (KL-BEM) orthogonal time frequency space (OTFS) receiver with superimposed pilots has been proposed for high-mobility communications with Doppler spread channel. First, an initial KL-BEM channel estimation is conducted by superimposed pilots, followed by the removal of superimposed pilots from the received OTFS signal and equalisation by message passing (MP) algorithm. After that, the detected data symbols are utilized as pseudo pilots along with the superimposed pilots to refine both KL-BEM channel estimation and equalisation in an iterative manner. Simulation results confirm the superior performance of the proposed KL-BEM OTFS receiver over the prior art in terms of the mean-square-error (MSE) of channel estimation and bit error rate (BER). It also has a close BER performance to the BER lower bound obtained by assuming perfect channel estimation. It contributes to high spectral efficiency and fast convergence performance.

Inventors

Yujie Liu
David González González
Yong Liang Guan

Assignees

Continental Automotive Technologies GmbH
NANYANG TECHNOLOGICAL UNIVERSITY

Dates

Publication Date: 20260512
Application Date: 20221026
Priority Date: 20211027

Claims (13)

1 . A receiver for an orthogonal time frequency space (OTFS) transmission system comprising a first receiver-side transformation unit and a second receiver-side transformation unit, a Karhunen-Loeve Basis Expansion Modeling (KL-BEM) channel estimation unit, a pilot removal unit, and an equaliser unit, wherein the receiver is adapted to receive, at an input of the first receiver-side transformation unit, a time-domain signal representing a communication frame comprising data signals and pilots superimposed thereon, transmitted over a communication channel, wherein the first receiver-side transformation unit is adapted to output a two-dimensional representation of the received communication frame in the time-frequency domain, wherein the output of the first receiver-side transformation unit is provided to an input of the second receiver-side transformation unit, which outputs a two-dimensional representation of the received communication frame comprising data signals and superimposed pilots in the delay-Doppler domain, wherein the output of the second receiver-side transformation unit is connected to a first input of the Karhunen-Loeve Basis Expansion Modeling (KL-BEM) channel estimation unit, which receives, at a second input, a signal (x p ) representing the superimposed pilots, and which outputs an estimation (Ĥ t i ) of the time-domain channel matrix, wherein the output of the KL-BEM estimation unit, along with the output of the second receiver-side transformation unit, is connected to respective inputs of the pilot removal unit, which is adapted to remove the superimposed pilots from the received signal (y) output from the second receiver-side transformation unit, and which outputs a signal representing an estimation of the only the data comprised in the received two-dimensional transmission frame in the delay-Doppler domain, wherein the output of the pilot removal unit is connected to the equaliser unit, which is adapted to output an estimated set of data signals ({circumflex over (x)} d i ), wherein the output of the equaliser unit is fed back to a third input of the KL-BEM channel estimation unit, wherein the receiver is adapted to iteratively repeat the channel estimation in the KL-BEM channel estimation unit, which is further adapted to, in the iterations, determine further estimations (Ĥ t i≥1 ) of the time-domain channel matrix based on the received signal (y) output from the second receiver-side transformation unit, the signal (x p ) representing the superimposed pilots, and the previously estimated set of data signals ({circumflex over (x)} d i ), to remove the superimposed pilots from the received signal (y) output from the second receiver-side transformation unit in the pilot removal unit, and to estimate a set of data signals ({circumflex over (x)} d i≥1 ) in the equaliser unit, until a termination criterion is met.
2 . The receiver according to claim 1 for an OTFS transmission system, wherein the first receiver-side transformation unit is adapted to perform a finite Fourier transform, an inverse Heisenberg- or Wigner-transform.
3 . The receiver according to claim 1 for an OTFS transmission system, wherein the second receiver-side transformation unit is adapted to perform a decoding and/or a symplectic finite Fourier transform.
4 . The receiver according to claim 1 for an OTFS transmission system, wherein the equaliser unit performs a message passing, a zero-forcing and/or a minimum mean square error equalisation.
5 . The receiver according to claim 1 for an OTFS transmission system, further comprising a control unit that is adapted to receive information about an absolute speed and direction of the receiver over ground, an absolute speed and direction of a transmitter over ground and/or a relative speed between the receiver ( 300 ) and the transmitter, and is further adapted to pass the received information to the KL-BEM channel estimation unit.
6 . The receiver according to claim 1 for an OTFS transmission system, further comprising a control unit that is adapted to receive information about the power allocation ratio used for a transmission frame, and is further adapted to pass the received information to the KL-BEM channel estimation unit and/or to the pilot removal unit.
7 . A wireless device comprising a receiver for an OTFS transmission system according to claim 1 .
8 . A method of receiving a binary data sequence over an orthogonal time frequency space (OTFS) communication channel susceptive to doubly-selective fading, comprising: receiving, over the communication channel, a continuous time-domain signal representing a communication frame comprising data signals and pilots superimposed thereon, transforming, in a first receiver-side transformation unit, the continuous time-domain signal representing the communication frame into a two-dimensional arrangement of information symbols in the time-frequency domain that is available at an output of the first receiver-side transformation unit, transforming, in a second receiver-side transformation unit, the two-dimensional arrangement of information symbols comprising pilot and data signals in the time-frequency domain into a two-dimensional communication frame comprising data signals and superimposed pilots, in the delay-Doppler domain, that is available at an output of the second receiver-side transformation unit, i) providing the signal output from the second receiver-side transformation unit and a signal (x p ) representing the superimposed pilots to a Karhunen-Loeve Basis Expansion Modeling (KL-BEM) channel estimation unit, for obtaining an estimation of the time-domain channel matrix (Ĥ t i ) at an output of the KL-BEM channel estimation unit, ii) providing the estimation of the time-domain channel matrix (Ĥ t i ) as well as the signal output from the second receiver-side transformation unit to a pilot removal unit, for removing the superimposed pilots from the received signal (y) output from the second receiver-side transformation unit, iii) providing the signal output from pilot removal unit to an equaliser unit, for obtaining an estimated set ({circumflex over (x)} d i ) of data signals at an output of the equaliser unit, iv) checking if a termination criterion is met, and if the termination criterion is not met, v) providing the previously estimated set ({circumflex over (x)} d i ) of data signals to the KL-BEM channel estimation unit and repeating steps i) to iv), or, if the termination criterion is met, outputting the previously estimated set (xd′) of data signals to a demapper, for obtaining binary data transmitted in the received communication frame.
9 . The method of claim 8 , wherein the first transforming step comprises subjecting the continuous time-domain signal representing a communication frame to a finite Fourier transform, an inverse Heisenberg-, or Wigner-transform.
10 . The method of claim 8 , wherein the second transforming step comprises subjecting the two-dimensional arrangement of information symbols comprising pilot and data signals in the time-frequency domain to a symplectic finite Fourier transform.
11 . The method of claim 8 , wherein obtaining an estimated set of data signals in the equaliser unit comprises subjecting the signal output from pilot removal unit to a message passing, a zero-forcing and/or a minimum mean square error equalisation.
12 . The method of claim 8 , further comprising: receiving, in a control unit, information about an absolute speed and direction of the receiver over ground, an absolute speed and direction of a transmitter over ground and/or a relative speed between the receiver and the transmitter, determining KL-BEM parameters to be used in the channel estimation unit, and providing the respective determined KL-BEM parameters to the channel estimation unit.
13 . A non-transitory computer readable medium storing a computer program product comprising computer program instructions which, when executed by a microprocessor, cause the computer and/or control hardware components of a receiver of an orthogonal time frequency space (OTFS) transmission system in accordance claim 1 to execute a method of receiving a binary data sequence over an OTFS communication channel susceptive to doubly-selective fading, comprising: receiving, over the communication channel, a continuous time-domain signal representing a communication frame comprising data signals and pilots superimposed thereon, transforming, in the first receiver-side transformation unit, the continuous time-domain signal representing the communication frame into a two-dimensional arrangement of information symbols in the time-frequency domain that is available at the output of the first receiver-side transformation unit, transforming, in the second receiver-side transformation unit, the two-dimensional arrangement of information symbols comprising pilot and data signals in the time-frequency domain into a two-dimensional communication frame comprising data signals and superimposed pilots, in the delay-Doppler domain, that is available at the output of the second receiver-side transformation unit, i) providing the signal output from the second receiver-side transformation unit and a signal representing the superimposed pilots to a Karhunen-Loeve Basis Expansion Modeling (KL-BEM) channel estimation unit, for obtaining an estimation of the time-domain channel matrix at the output of the KL-BEM channel estimation unit, ii) providing the estimation of the time-domain channel matrix as well as the signal output from the second receiver-side transformation unit to the pilot removal unit, for removing the superimposed pilots from the received signal output from the second receiver-side transformation unit, iii) providing the signal output from pilot removal unit to the equaliser unit, for obtaining an estimated set of data signals at an output of the equaliser unit, iv) checking if a termination criterion is met, and if the termination criterion is not met, v) providing the previously estimated set of data signals to the KL-BEM channel estimation unit and repeating steps i) to iv), or, if the termination criterion is met, outputting the previously estimated set of data signals to a demapper, for obtaining binary data transmitted in the received communication frame.

Description

CROSS REFERENCE TO RELATED APPLICATIONS This application is the U.S. National Phase Application of PCT International Application No. PCT/EP2022/079857, filed Oct. 26, 2022, which claims priority to German Application No. 10 2022 106 409.3, filed Mar. 18, 2022 and German Application No. 10 2021 212 161.6, filed Oct. 27, 2021, the contents of such applications being incorporated by reference herein. FIELD OF THE INVENTION The present invention relates to a method of receiving symbols over an orthogonal time frequency space (OTFS) communication channel subject to Doppler spread and a receiver implementing the method. BACKGROUND The sixth generation (6G) wireless communications and beyond are expected to serve a large number of high-mobility users, e.g., vehicles, subways, highways, trains, drones, low earth orbit (LEO) satellites, etc. The preceding fourth and fifth generation (5G) wireless communications use orthogonal frequency division multiplexing (OFDM), which provides high spectral efficiency and high robustness against frequency selective fading channel, and also allow for using low-complexity equalisers. However, due to speed-dependent Doppler shifts or spreads and quickly varying multipath reception, high-mobility communications suffer from severe time and frequency dispersiveness. Time and frequency dispersiveness each cause signal fading at the receiver, and the fading is thus also referred to as doubly selective channel fading. Doubly selective channel fading significantly impairs the performance of OFDM communication. As an alternative to OFDM, OTFS modulation was proposed as a solution for coping with doubly selective fading channels. OTFS modulation is a 2D modulation scheme that multiplexes information QAM symbols over carrier waveforms that correspond to localized pulses in a signal representation that is referred to as delay-Doppler representation. The OTFS waveforms are spread over both time and frequency while remaining roughly orthogonal to each other under general delay-Doppler channel impairments. In theory, OTFS combines the reliability and robustness of spread spectrum with the high spectral efficiency and low complexity of narrowband transmission. The OTFS waveforms couple with the wireless channel in a way that directly captures the underlying physics, yielding a high-resolution delay-Doppler Radar image of the constituent reflectors. As a result, the time-frequency selective channel is converted into an invariant, separable and orthogonal interaction, where all received symbols experience the same localized impairment and all the delay-Doppler diversity branches are coherently combined. This renders OTFS ideally suited for wireless communication between transmitters and receivers that move at high speeds with respect to each other, e.g., receivers or transmitters located in high-speed trains, cars and even aircrafts. However, OTFS presents its own challenges when it comes to channel estimation and equalisation in a receiver, and using adapted conventional OFDM receiver designs does not provide the required performance, requires significant pilot overhead of up to 50%, or provides acceptable performance only under ideal conditions, which are unrealistic in practice. Throughout this specification, bold symbols represent vectors or matrices. Superscripts T, H and †, respectively denote the transpose, complex conjugate transpose and pseudo inverse of a vector or matrix. diag {a} is a diagonal matrix with vector a on its diagonal, while diag {A} is a vector whose elements are from the diagonal of matrix A. ⊗ is the Kronecker product. SUMMARY OF THE INVENTION An aspect of the present invention includes proposing a receiver for an OTFS transmission system and a corresponding method for receiving binary data sequences over an OTFS communication channel, in particular in OTFS communication channels having long delay spread and large Doppler spread, the receiver and method permitting using communication frames having a small pilot overhead or requiring no dedicated pilot slots at all while providing near-optimal performance from transmission to decoding. The various aspects of the present invention rely on a novel model representing an OTFS channel, which will be introduced prior to discussing the application thereof in the novel receiver and the corresponding method for receiving. FIG. 1 shows a block diagram of a general OTFS transmission system. A transmitter 200 comprises 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) that outputs a two-dimensional sequence of information symbols x[k, l] in which the QAM symbols are arranged along the delay period and the Doppler period of the delay-Doppler domain. The information symbols comprise data symbols, pilot symbols and guard symbols surrounding the pilot symbols. The two-dimensional sequence of information symbols x[k