Receiver for and method of receiving symbols over time varying channels with Doppler spread

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.

Claims

1. A receiver for an OTFS transmission system comprising a first receiver-side transformation unit and a second receiver-side transformation 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, characterised in that wherein the output of the second receiver-side transformation unit is connected to a first input of a KL-BEM channel estimation unit, which receives, at a second input, a signal (x.sub.p) representing the superimposed pilots, and which outputs an estimation (.sub.t.sup.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 a 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 an equaliser unit, which is adapted to output an estimated set of data signals ({circumflex over (x)}.sub.d.sup.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 (.sub.t.sup.i1) of the time-domain channel matrix based on the received signal (y) output from the second receiver-side transformation unit, the signal (x.sub.p) representing the superimposed pilots, and the previously estimated set of data signals ({circumflex over (x)}.sub.d.sup.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 (.sub.d.sup.i1) 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 the absolute speed and direction of the receiver over ground, the absolute speed and direction of the transmitter over ground and/or the 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 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.sub.p) representing the superimposed pilots to a KL-BEM channel estimation unit, for obtaining an estimation of the time-domain channel matrix (.sub.t.sup.i) at an output of the KL-BEM channel estimation unit, ii) providing the estimation of the time-domain channel matrix (.sub.t.sup.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)}.sub.d.sup.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)}.sub.d.sup.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 ({circumflex over (x)}.sub.d.sup.i) 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 the absolute speed and direction of the receiver over ground, the absolute speed and direction of the transmitter over ground and/or the 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 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 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 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.

14. A computer readable medium or data carrier retrievably transmitting or storing the computer program product of claim 13.

Description

BRIEF DESCRIPTION OF THE DRAWING

[0085] In the following section exemplary embodiments of the invention will be described in greater detail with reference to the drawing. In the drawing,

[0086] FIG. 1 shows a block diagram of a general OTFS transmission system,

[0087] FIG. 2 schematically shows the superimposed pilots and their power allocation,

[0088] FIG. 3 shows a block diagram of channel estimation and equalisation of an exemplary receiver in accordance with an aspect of the present invention,

[0089] FIG. 4 shows a representation of the BER over the BEM-order of a KL-BEM receiver in accordance with an aspect of the invention,

[0090] FIGS. 5A and 5B show a comparison of the channel estimation error and the BER over SNR for various OTFS receivers,

[0091] FIG. 6 shows a comparison of the BER over the number of iterations for various OTFS receivers,

[0092] FIG. 7 shows the BER performance of the proposed KL-BEM OTFS receiver and existing superimposed pilot-aided OTFS receiver as a function the pilot power allocation ratio with SNR=12 dB,

[0093] FIG. 8 shows a flow diagram of a method of receiving a binary data sequence over an OTFS communication channel susceptive to doubly-selective fading.

[0094] Throughout the figures identical or similar elements may be referenced using the same reference designators.

DESCRIPTION OF EMBODIMENTS

[0095] FIGS. 1, 2 and 4 to 7 have been described further above and will not be discussed again.

[0096] FIG. 3 shows a block diagram of channel estimation and equalisation of an exemplary KL-BEM OTFS receiver in accordance with an aspect of the present invention. The channel estimation and equalisation replace the generic channel estimation and equalisation block 310 shown in FIG. 1. All other elements of the receiver 300 shown in FIG. 1, i.e., first and second receiver-side transformation units 304 and 306, respectively, are identical and are not shown in the figure.

[0097] The two-dimensional arrangement of data signals and superimposed pilots y [k,l] in the delay-Doppler domain output from the second receiver-side transformation unit 306 is applied at a first input of a KL-BEM channel estimation unit 320, and is also provided to an input of a pilot removal unit 322. KL-BEM channel estimation unit 320 performs an initial channel estimation based on the superimposed pilots x.sub.p, the arrangement and power level of which are known to the KL-BEM channel estimation unit 320 and, in subsequent iterations, performs further channel estimations using estimations {circumflex over (x)}.sub.d.sup.i of the transmitted symbols fed back to KL-BEM channel estimation unit 320 from equaliser unit 324 as pseudo pilots in addition to the superimposed pilots. The output of the KL-BEM channel estimation unit 320, which represents a channel estimation .sub.t.sup.i, is input to the pilot-removal unit 322. Based thereon, pilot removal unit 322 removes the superimposed pilots from the received signal vector y [k, l] in the delay-Doppler domain, and provides an estimation of a signal representing only the received data signal .sub.d.sup.i, to an input of equaliser unit 324. Equaliser unit 324 outputs estimations {circumflex over (x)}.sub.d.sup.i of the transmitted data symbols. Iterations may be repeated until a termination criterion is fulfilled.

[0098] FIG. 8 shows a flow diagram of a method 500 of receiving a binary data sequence over an OTFS communication channel susceptive to doubly-selective fading. In step 502 a continuous time-domain signal representing a communication frame is received over the communication channel. In step 504 the continuous time-domain signal representing the communication frame is transformed into a two-dimensional arrangement of information symbols in the time-frequency domain. In step 506 the two-dimensional arrangement of information symbols comprising data signals and superimposed pilots in the time-frequency domain is transformed into a two-dimensional communication frame comprising data signals and superimposed pilots in the delay-Doppler domain. In step 508 an initial estimation of a time-domain channel matrix is obtained in a KL-BEM channel estimation unit 320 that performs a channel estimation based on a Karhunen-Loeve basis expansion modelling of the time-varying communication channel, using only the superimposed pilots. In step 510 the pilots are removed from the two-dimensional communication frame comprising data signals and superimposed pilots in the delay-Doppler domain obtained in step 506. The resulting signal, which represents an estimation of only the transmitted data signals, is subjected to an equalisation in step 512, for obtaining an estimated set of data signals. Step 514 checks if a termination criterion is met, which in the positive case, Yes-branch of step 514, signals that the estimated received symbols can be output to a de-mapper, in step 516, and ultimately can be output as a received binary sequence. If the termination criterion is not met, No-branch of step 514, the set of data signals a previously estimated in step 512 is fed to the KL-BEM channel estimation unit 320 in step 518, and steps 508 to 514 are repeated. The further estimations of time-domain channel matrices are based on data signals previously estimated in step 512 and the superimposed pilots.

DEFINITIONS AND LIST OF REFERENCE NUMERALS (PART OF THE DESCRIPTION)

[0099] f.sub.c carrier frequency [0100] f subcarrier spacing [0101] L channel length [0102] M number of delay bins [0103] N number of Doppler bins [0104] P.sub.T total transmission power [0105] pilot power allocation ratio [0106] pilot overhead [0107] Q.sub.S BEM order in the initial, low-order channel estimation [0108] Q.sub.L BEM order in the subsequent, iterative channel estimation [0109] AWGN additive white Gaussian noise [0110] BEM basis expansion model [0111] CE-BEM complex exponential BEM [0112] GCE-BEM generalized CE-BEM [0113] DFT discrete Fourier transform [0114] KL-BEM Karhunen-Loeve BEM [0115] MSE mean square error [0116] OTFS orthogonal time frequency space [0117] SNR signal-to-noise-ratio [0118] BER bit error rate [0119] OFDM orthogonal frequency division multiplexing [0120] MP message passing [0121] SFFT finite symplectic Fourier transform [0122] 200 transmitter [0123] 202 first transmitter-side transformation unit [0124] 204 second transmitter-side transformation unit [0125] 206 antenna [0126] 300 receiver [0127] 302 antenna [0128] 304 first receiver-side transformation unit [0129] 306 second receiver-side transformation unit [0130] 310 channel estimation and equalisation block [0131] 320 KL-BEM channel estimation unit [0132] 322 pilot removal unit [0133] 324 equaliser unit [0134] 500 method of receiving [0135] 502 receiving continuous time-domain signal [0136] 504 transforming continuous time-domain signal into a two-dimensional arrangement of information symbols in the time-frequency domain [0137] 506 transforming a two-dimensional arrangement of information symbols in the time-frequency domain into a two-dimensional communication frame in the delay-Doppler domain [0138] 508 estimating time-domain channel matrix in a KL-BEM channel estimation unit [0139] 510 removing pilots [0140] 512 estimating symbols [0141] 514 termination criterion met? [0142] 516 output estimation to de-mapper [0143] 518 feed estimated symbols to KL-BEM channel estimation