OTFS Waveform Design Method Based on 3D Constellation Mapper in High-Speed Mobile Scenarios

Abstract

The present invention discloses an OTFS waveform design method based on a three-dimensional constellation mapper in a high-speed mobile scenario, and proposes to apply three-dimensional constellation mapping technology in the OTFS system to improve the bit error performance under high-order modulation. Compared with the traditional two-dimensional modulation OTFS system, it has a lower bit error rate and a higher information transmission rate, and the proposed waveform is more suitable for high-speed mobile communication scenarios.

Description

Technical Field

[0001] The present invention relates to the field of communication technologies, and more specifically, to a method for designing an OTFS waveform based on a three-dimensional constellation mapper in a high-speed mobile scenario. Background Art

[0002] The high-speed mobile scenario is one of the important scenarios in current 5G and even future 6G wireless communication networks, such as high-speed rail communication, unmanned aerial vehicle communication, vehicle-to-everything communication, satellite-to-ground communication, etc. In a high-speed mobile scenario, the high-speed relative movement between the communication transceiver ends will cause the channel to change rapidly, making the channel exhibit the property of double dispersion, including time dispersion caused by multipath effects and frequency dispersion caused by Doppler frequency shift. The currently widely used air interface waveform technology - orthogonal frequency division multiplexing (OFDM) - can well resist the inter-symbol interference caused by time dispersion due to the introduction of a cyclic prefix (CP). However, in a high-speed mobile scenario, frequency dispersion will destroy the orthogonality between OFDM subcarriers, causing inter-carrier interference (ICI), and thus seriously damaging the communication performance of the OFDM system. Therefore, it is necessary to introduce a new air interface waveform that can effectively solve the performance loss problem caused by Doppler frequency offset in a high-speed mobile scenario.

[0003] In the above background, the orthogonal time-frequency-space (OTFS) waveform technology proposed by R. HADAN et al. is expected to solve the Doppler frequency offset problem faced in a high-speed mobile scenario. This technology modulates data in the time-delay Doppler domain, converting the double-dispersion time-frequency domain channel into an approximately stationary sparse time-delay Doppler domain channel, so that the OTFS symbols experience approximately equal channel gains. Therefore, as a new waveform, OTFS has strong robustness to time-varying channels. At the same time, the OTFS system can be implemented by adding a pre / post processing module to the existing air interface waveform OFDM system, enabling OTFS to have good compatibility with the OFDM system. In addition, existing research shows that OTFS can be well combined with important communication technologies such as millimeter-wave (mmWave) communication, non-orthogonal multiple access (NOMA), and intelligent reflecting surface (IRS). Therefore, the OTFS waveform has broad application prospects.

[0004] At present, most of the OTFS waveform modulation technologies use QAM two-dimensional constellation diagrams for symbol mapping, and the two-dimensional constellation diagrams have obvious defects. When the modulation order increases, the minimum Euclidean distance between constellation points in the constellation diagram will significantly decrease (note that this is the case where the symbols in the constellation diagram have the same transmission power), and this will lead to a significant deterioration in the communication performance of the receiving part of the system. At present, the bit error performance at higher modulation orders can be improved by optimizing the equalization and detection algorithms at the receiving end, but this will greatly increase the implementation difficulty at the receiving end and consume more hardware costs. Therefore, improving the performance of the OTFS system at higher modulation orders from the receiving end is not an optimal method to achieve a balance between performance and cost. Summary of the Invention

[0005] The present invention provides an OTFS waveform design method based on a three-dimensional constellation mapper in a high-speed mobile scenario to improve the bit error performance under high-order modulation.

[0006] To solve the above technical problems, the technical solution of the present invention is as follows:

[0007] An OTFS waveform design method based on a three-dimensional constellation mapper in a high-speed mobile scenario has the following steps at the transmitting end:

[0008] S1: Perform serial / parallel conversion on the binary bit stream to obtain parallel bits;

[0009] S2: Apply three-dimensional constellation mapping technology to perform constellation mapping on the parallel bits to obtain mapped three-dimensional symbols;

[0010] S3: Perform I / Q transformation operation on the mapped three-dimensional symbols to convert them into I / Q complex symbols;

[0011] S4: Place the I / Q complex symbols in the time-delay Doppler lattice and use zero padding to generate the OTFS data block to be modulated;

[0012] S5: Perform OTFS modulation on the OTFS data block, add CP, and send it to the extended vehicle signal for transmission;

[0013] The following steps are carried out at the receiving end:

[0014] S6: After receiving the signal and removing the CP, perform demodulation through the OTFS demodulator to obtain the demodulated signal;

[0015] S7: Perform symbol detection on the demodulated signal using a minimum mean square error detector to obtain the detected I / Q symbols. The channel matrix used in the minimum mean square error detector is obtained through signal estimation, and it is assumed that the complete channel state information is obtained through estimation;

[0016] S8: Perform tail zero-discarding processing on the detected I / Q symbols;

[0017] S9: Perform three-dimensional transformation operation on the zero-discarded I / Q symbols to convert them into three-dimensional symbols;

[0018] S10: Use three-dimensional constellation demapping technology to perform three-dimensional demapping on the three-dimensional symbols and convert them into parallel bits;

[0019] S11: Obtain an estimated value of the serial binary data bit stream by performing parallel-to-serial conversion on the parallel bits.

[0020] Preferably, in step S1, the binary bit stream is converted from serial to parallel to parallel bits, specifically:

[0021] Consider an OTFS system with a data block containing N subcarriers and M symbols, and x binary bit stream data to be modulated x = (b0, b1, b2,..., b x-1 ), according to the size of the modulation order Q, the binary bit stream is converted from serial to parallel to obtain an MN×1 parallel symbol vector s = (s0, s1, s2,..., s MN-1 ) T .

[0022] Preferably, in step S2, the three-dimensional constellation mapping technology is applied to perform constellation mapping on the parallel bits to obtain the mapped three-dimensional symbols, specifically:

[0023]

[0024] In the formula, x i , y i , z i , i = 0,..., MN - 1 are the three-dimensional coordinates of the constellation points in the Q-order three-dimensional constellation diagram.

[0025] Preferably, in step S3, the mapped three-dimensional symbols are converted into I / Q complex symbols by performing I / Q transformation operation, specifically:

[0026]

[0027] In the formula, P is the number of complex signals in the I / Q matrix, P = (3 / 2)×MN.

[0028] Preferably, in step S4, the I / Q complex symbols are placed in the time-delay Doppler lattice and zero-padding is used to generate the OTFS data block to be modulated, specifically:

[0029] In the time-delay Doppler domain, there are M' time-delay grid points along the time-delay axis and N' Doppler grid points along the Doppler axis. Let the time-delay grid points and the Doppler grid points be equal, i.e., M' = N'. At this time, the OTFS data block becomes a square matrix, and let the dimension of this square matrix be where represents taking the integer upper bound. Among them, the grid points in the OTFS data block where the complex signal is not placed are filled with zeros. After zero filling, the matrix form of the OTFS data block is as follows:

[0030]

[0031] In the formula, s is the complex signal vector in X I / Q . The subscripts of s represent the Doppler grid point position and the time-delay grid point position in the time-delay Doppler grid points respectively.

[0032] Preferably, in step S5, the OTFS data block is subjected to OTFS modulation, CP is added, and then sent to the extended vehicle signal for transmission. Specifically:

[0033] The OTFS data block can be expressed after the inverse symplectic Fourier transform as:

[0034] X TF = F M' X DD F N' H

[0035] In the formula, F N is the N-point Fourier transform matrix, (.) H represents taking the conjugate transpose, and TF represents the time-frequency domain;

[0036] The signal X TF in the time-frequency domain is converted into a time-domain signal S after the inverse discrete Fourier transform:

[0037] S = F M' H X TF

[0038] The time-domain signal S is vectorized to obtain the signal s to be transmitted after modulation:

[0039] s = vec(S) = vec(X DD F N' H )

[0040] The signal after OTFS modulation is added with CP and then sent to the extended vehicle channel for transmission.

[0041] Preferably, in step S6, after receiving the signal and removing the CP, it is demodulated by an OTFS demodulator to obtain the demodulated signal. Specifically:

[0042] After removing the cyclic prefix (CP) from the received signal \(r\), it is expressed as:

[0043] \(r = Hs+w\)

[0044] where \(H\) represents the channel matrix, \(w\) represents the additive white Gaussian noise, and \(w\sim CN(0,\sigma 2 I M'N' );

[0045] The received signal \(r\) is successively subjected to discrete Fourier transform and symplectic Fourier transform to obtain the received signal in the time-delay Doppler domain, which is expressed as follows:

[0046] \(Y = F M H F M' RF N' = RF N'

[0047] In the formula, \(R\) is the matrix form of the received signal \(r\) after recombination, and its dimension is \(M'\times N'\);

[0048] The input-output relationship in the time-delay Doppler domain can be represented by vectorizing the received signal \(Y\):

[0049]

[0050] In the formula, \(H eff and are the equivalent channel matrix and the equivalent noise vector respectively, represents the Kronecker product.

[0051] Preferably, in step S7, the channel matrix formed by the complete channel state information obtained through channel estimation by the minimum mean square error detector is the equivalent channel matrix \(H\) in step S6 eff , and the symbol estimation result in the time-delay Doppler domain obtained after detection by the minimum mean square error detector is:

[0052]

[0053] Preferably, the number of symbols with 0 discarded in step S8 is \(M'N'-MN\).

[0054] Preferably, in step S9, the complex signals of the I / Q two-way transmission estimated at the receiving end are converted into three-dimensional symbol coordinates in a three-dimensional constellation diagram through a transformation matrix; in step S10, the minimum distance decision is used to demap the three-dimensional symbols into parallel bits; in step S11, the parallel bits obtained by demapping are converted through parallel / serial conversion to obtain the estimated value of the binary bit stream.

[0055] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0056] The present invention proposes to apply three-dimensional constellation mapping technology in the OTFS system to improve the bit error performance under high-order modulation. Compared with the traditional two-dimensional modulation OTFS system, it has a lower bit error rate and a higher information transmission rate, and makes the OTFS system more suitable for high-speed mobile communication scenarios. Brief Description of the Drawings

[0057] Figure 1 It is a schematic flowchart of the method of the present invention.

[0058] Figure 2 It is a transceiver block diagram of the 3D-OTFS system described in the present invention provided for the embodiment.

[0059] Figure 3 It is a constellation mapping diagram in the three-dimensional constellation mapping described in the present invention provided for the embodiment.

[0060] Figure 4 It is a schematic diagram of the OTFS modulation and demodulation process described in the present invention provided for the embodiment.

[0061] Figure 5 It is a schematic diagram of the delay-Doppler lattice points provided for the embodiment.

[0062] Figure 6 It is a schematic diagram for comparing the BER performance of the proposed 3D-OTFS scheme and the traditional OTFS scheme of the present invention under different modulation orders provided for the embodiment.

[0063] Figure 7 It is a schematic diagram for comparing the BER performance of the proposed 3D-OTFS scheme and the traditional OTFS scheme of the present invention under another different modulation orders provided for the embodiment.

[0064] Figure 8 It is a schematic diagram for comparing the BER performance of the proposed 3D-OTFS scheme and the traditional OTFS scheme of the present invention under different modulation orders in a static flat fading channel provided for the embodiment. Detailed Embodiment

[0065] The drawings are only for illustrative purposes and should not be construed as a limitation of this patent;

[0066] In order to better illustrate this embodiment, some components in the drawings are omitted, enlarged or reduced, and do not represent the dimensions of the actual product;

[0067] For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0068] The technical solutions of the present invention will be further described below with reference to the drawings and embodiments.

[0069] Embodiment 1

[0070] This embodiment provides a method for designing OTFS waveforms based on a three-dimensional constellation mapper in a high-speed mobile scenario. As Figure 1 shown, the following steps are performed at the transmitter:

[0071] S1: Convert the binary bit stream through serial / parallel conversion into parallel bits;

[0072] S2: Apply three-dimensional constellation mapping technology to perform constellation mapping on the parallel bits to obtain the mapped three-dimensional symbols;

[0073] S3: Perform I / Q transformation operation on the mapped three-dimensional symbols to convert them into I / Q complex symbols;

[0074] S4: Place the I / Q complex symbols in the time-delay Doppler lattice and use zero-padding to generate the OTFS data block to be modulated;

[0075] S5: Modulate the OTFS data block by OTFS, add CP, and send it to the extended vehicle signal for transmission;

[0076] The following steps are performed at the receiver:

[0077] S6: After receiving the signal and removing the CP, demodulate it through an OTFS demodulator to obtain the demodulated signal;

[0078] S7: Perform symbol detection on the demodulated signal using a minimum mean square error detector to obtain the detected I / Q symbols. The channel matrix used in the minimum mean square error detector is obtained through signal estimation, and it is assumed that the complete channel state information is obtained through estimation;

[0079] S8: Perform a zero-discarding process on the trailing zeros of the detected I / Q symbols;

[0080] S9: Perform a three-dimensional transformation operation on the I / Q symbols after the zero-discarding process to convert them into three-dimensional symbols;

[0081] S10: Use three-dimensional constellation demapping technology to perform three-dimensional demapping on the three-dimensional symbols to convert them into parallel bits;

[0082] S11: Convert the parallel bits through parallel / serial conversion to obtain an estimated value of the serial binary data bit stream.

[0083] The transceiver block diagram of the 3D-OTFS system described in the present invention is as Figure 2 shown; the constellation mapping diagram in the three-dimensional constellation mapping described in the present invention is as Figure 3 shown; the OTFS modulation and demodulation process described in the present invention is as Figure 4 shown.

[0084] Embodiment 2

[0085] Based on Embodiment 1, the following content is further disclosed in this embodiment:

[0086] In step S1, the binary bit stream is converted from serial to parallel to parallel bits, specifically:

[0087] Consider an OTFS system with a data block containing N subcarriers and M symbols, and x binary bit stream data to be modulated, x = (b0, b1, b2,..., b x-1 ), according to the size of the modulation order Q, the binary bit stream is converted from serial to parallel to obtain a parallel symbol vector s = (s0, s1, s2,..., s MN-1 ) T .

[0088] In step S2, the three-dimensional constellation mapping technology is applied to perform constellation mapping on the parallel bits to obtain the mapped three-dimensional symbols. As Figure 2 shown, by sequentially mapping the MN×1 parallel symbol vector to the Figure 2 shown Q-order three-dimensional constellation diagram, the value of Q is 4, 16, 64, 128, 256, 512, corresponding to three-dimensional constellation diagrams with different numbers of constellation points respectively. The three-dimensional symbol coordinate matrix formed by the mapped three-dimensional constellation points is specifically:

[0089]

[0090] In the formula, x i , y i , z i , i = 0,..., MN-1 are the three-dimensional coordinates of the constellation points in the Q-order three-dimensional constellation diagram.

[0091] In step S3, the mapped three-dimensional symbols are subjected to I / Q transformation operations to be converted into I / Q complex symbols, specifically:

[0092]

[0093] In the formula, P is the number of complex signals in the I / Q matrix, P = (3 / 2)×MN.

[0094] In step S4, the I / Q complex symbols are placed in the time-delay Doppler lattice and zero-padding is used to generate the OTFS data block to be modulated, specifically:

[0095] As Figure 5As shown, there are M' delay grid points along the delay axis and N' Doppler grid points along the Doppler axis in the time-delay Doppler domain. Since P complex signals need to be placed in the time-delay Doppler grid points, first make the delay grid points and Doppler grid points equal, i.e., M' = N'. At this time, the OTFS data block becomes a square matrix, and let the dimension of this square matrix be where represents taking the integer upper bound. Among them, the grid points in the OTFS data block where no complex signals are placed are filled with zeros. After zero-padding, the matrix form of the OTFS data block is as follows:

[0096]

[0097] In the formula, s is the complex signal vector in X I / Q . The subscripts of s represent the Doppler grid point position and the delay grid point position in the time-delay Doppler grid points respectively.

[0098] The specific steps of S5 and S6 are the OTFS modulation and demodulation processes of the OTFS data block. The OTFS modulation and demodulation processes can be realized by adding a pre-processing module and a post-processing module to the OFDM modulation scheme. Among them, the pre-processing module is the inverse symplectic Fourier transform (ISFFT), and the post-processing module is the symplectic Fourier transform (SFFT). Specifically as follows:

[0099] In step S5, the OTFS data block is subjected to OTFS modulation, CP is added, and then sent to the extended vehicle signal for transmission. Specifically:

[0100] After the OTFS data block passes through the inverse symplectic Fourier transform, it can be expressed as:

[0101] X TF = F M' X DD F N' H

[0102] In the formula, F N is the N-point Fourier transform matrix, (.) H represents taking the conjugate transpose, and TF represents the time-frequency domain;

[0103] The time-frequency domain signal X TF is converted into a time-domain signal S after passing through the inverse discrete Fourier transform (IDFT):

[0104] S = F M' H X TF

[0105] The time-domain signal S is vectorized to obtain the signal s to be transmitted after modulation:

[0106] s = vec(S) = vec(X DD F N' H )

[0107] Add a CP to the signal after completing the OTFS modulation and send it to the extended vehicle channel for transmission.

[0108] After receiving the signal and removing the CP in step S6, demodulate it through the OTFS demodulator to obtain the demodulated signal, specifically:

[0109] The received signal r after removing the CP is expressed as:

[0110] r = Hs + w

[0111] where H represents the channel matrix, w represents additive white Gaussian noise (AWGN), and satisfies w ~ CN(0, σ 2 I M'N' );

[0112] Perform a discrete Fourier transform (DFT) and a symplectic Fourier transform (SFFT) on the received signal r in sequence to obtain the received signal in the time-delay Doppler domain, expressed as follows:

[0113] Y = F M H F M' RF N' = RF N'

[0114] In the formula, R is the matrix form of the received signal r after recombination, and its dimension is M'×N';

[0115] The input-output relationship in the time-delay Doppler domain can be represented by vectorizing the received signal Y:

[0116]

[0117] In the formula, H eff and are the equivalent channel matrix and the equivalent noise vector respectively, represents the Kronecker product.

[0118] In step S7, the channel matrix formed by the complete channel state information obtained through channel estimation by the minimum mean square error detector is the equivalent channel matrix H in step S6 eff , and the time-delay Doppler domain symbol estimation result obtained after detection by the minimum mean square error detector is:

[0119]

[0120] In step S8, the number of symbols discarded as 0 is M'N' - MN.

[0121] Steps S9, S10, and S11 are the inverse operations of steps S3, S2, and S1, respectively, as follows:

[0122] In step S9, the complex signals transmitted on the I / Q channels estimated by the receiver are converted into three-dimensional symbol coordinates in a three-dimensional constellation diagram through a transformation matrix; in step S10, minimum distance decision is used to demap the three-dimensional symbols into parallel bits; in step S11, the demapped parallel bits are converted from parallel to serial to obtain an estimated binary bit stream.

[0123] Embodiment 3

[0124] The following embodiments are specifically disclosed in this embodiment:

[0125] In the specific implementation process, the simulation parameters are set as follows: Consider an OTFS system with a data block containing 8 subcarriers and 8 symbols, where the carrier frequency is 4 GHz, the subcarrier spacing is 15 KHz, the three-dimensional constellation mappings have 4 points (4-ary), 16 points (16-ary), 64 points (64-ary), 128 points (128-ary), 256 points (256-ary), and 512 points (512-ary), the relative moving speed of the communication terminal is 500 Km / h, the maximum Doppler shift is 1850 Hz, the channel estimation is assumed to be ideal, the wireless channel is set to the Extended Vehicular A (EVA) model, the multipath delays are [0, 30, 150, 310, 370, 710, 1090, 1730, 2510] ns, and the normalized powers are [0, -1.5, -1.4, -3.6, -0.6, -9.1, -7, -12, -16.9] dB.

[0126] Specifically, the BER performance of the proposed 3D-OTFS scheme of the present invention is compared with that of the traditional OTFS scheme under different modulation orders. According to Figure 6 and Figure 7As shown, in the BER performance on the EVA channel, the BER performance of the 3D-OTFS scheme proposed by the present invention is significantly better than that of the traditional OTFS scheme. It can also be noted that as the modulation order increases from 4 to 128, for the same bit error rate, the signal-to-noise ratio (SNR) required by 3D-OTFS is significantly reduced compared to traditional OTFS. In other words, the improvement in the bit error performance of 3D-OTFS compared to OTFS increases with the increase in the modulation order and reaches an improvement of nearly 5 dB. When the modulation order increases from 128 to 512, the improvement in the bit error performance of 3D-OTFS is no longer obvious and remains within the range of 3 - 5 dB. It can also be noted that as the SNR increases, the bit error performance of 3D-OTFS gradually improves compared to traditional OTFS. At the same time, due to the increase in the modulation order, on the premise of the same bit error, the information transmission rate can be further improved.

[0127] The above embodiments show that the method of the present invention has a lower bit error rate and a higher information transmission rate compared to the traditional OTFS modulation scheme, and improves the bit error performance of OTFS under high-order modulation.

[0128] More specifically, based on Example 1, the BER performance of the present invention in a static flat fading channel is discussed.

[0129] According to Figure 8 As shown, in the BER performance on the static flat fading channel, under different modulation orders, the improvement in the BER performance of the 3D-OTFS scheme proposed by the present invention compared to the traditional OTFS scheme is not obvious. For the same bit error rate, the 3D-OTFS with a modulation order of 4 has almost no performance improvement compared to traditional OTFS, and as the modulation order increases, the improvement in the bit error performance is only within the range of 2 - 3 dB. As the SNR increases, the bit error performance of 3D-OTFS does not improve significantly. Based on the above discussion, 3D-OTFS has no obvious performance improvement in the static flat fading channel of non-high-speed mobile scenarios.

[0130] Combined with the above analysis of BER, it can be further shown that the 3D-OTFS waveform of the present invention can have a more obvious performance improvement in high-speed mobile scenarios. Therefore, the 3D-OTFS scheme proposed by the present invention can have a lower bit error rate and a higher information transmission rate, and is also more suitable for high-speed mobile communication scenarios.

[0131] The same or similar reference numerals correspond to the same or similar components;

[0132] The terms describing the positional relationship in the drawings are only for illustrative purposes and should not be construed as a limitation of this patent;

[0133] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, rather than limitations on the implementation manners of the present invention. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to enumerate all the implementation manners here. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the claims of the present invention.

Claims

1. A method for designing OTFS waveforms based on a three-dimensional constellation mapper in a high-speed mobile scenario, characterized in that, At the transmitting end, there are the following steps: S1: The binary bit stream is subjected to serial / parallel conversion into parallel bits; S2: Apply three-dimensional constellation mapping technology to perform constellation mapping on the parallel bits to obtain the mapped three-dimensional symbols; S3: Perform I / Q transformation operation on the mapped three-dimensional symbols to convert them into I / Q complex symbols; S4: Place the I / Q complex symbols in the delay-Doppler lattice and use zero-padding to generate the OTFS data block to be modulated; S5: Modulate the OTFS data block by OTFS, add CP, and send it into the extended vehicle signal for transmission; At the receiving end, there are the following steps: S6: After receiving the signal r and removing the CP, demodulate it through the OTFS demodulator to obtain the demodulated signal; S7: Use the minimum mean square error detector to perform symbol detection on the demodulated signal to obtain the detected I / Q symbols. The channel matrix used in the minimum mean square error detector is obtained through signal estimation, and it is assumed that the complete channel state information is obtained through estimation; S8: Perform the operation of discarding 0 at the tail on the detected I / Q symbols; S9: Perform three-dimensional transformation operation on the I / Q symbols after discarding 0 to convert them into three-dimensional symbols; S10: Use three-dimensional constellation demapping technology to perform three-dimensional demapping on the three-dimensional symbols to convert them into parallel bits; S11: Perform parallel / serial conversion on the parallel bits to obtain the estimated value of the serial binary data bit stream; Specifically: The received signal r after removing the CP is expressed as: r = Hv + w where \(H\) represents the channel matrix, \(w\) represents additive white Gaussian noise, and \(w\sim CN(0,\sigma 2 I M'N' \)), the time-domain signal \(V\) is vectorized to obtain the signal \(v\) to be transmitted after modulation; Perform discrete Fourier transform and symplectic Fourier transform on the received signal r in sequence to obtain the received signal in the delay-Doppler domain, which is expressed as follows: Y = F M' H F M' RF N' = RF N' where \(R\) is the matrix form of the received signal \(r\) after recombination, with dimensions \(M'\times N'\), \((.)\) H denotes taking the conjugate transpose; The input-output relationship in the delay-Doppler domain can be expressed by vectorizing the received signal Y: where, H eff and are the equivalent channel matrix and the equivalent noise vector respectively, denotes the Kronecker product.

2. The method for designing OTFS waveforms based on a three-dimensional constellation mapper in a high-speed mobile scenario according to claim 1, characterized in that, In step S1, the binary bit stream is subjected to serial / parallel conversion into parallel bits, specifically: Consider an OTFS system with a data block containing N subcarriers and M symbols, and an x-bit binary bitstream data to be modulated x = (b0, b1, b2,..., b x-1 ). According to the size of the modulation order Q, the binary bitstream is converted through serial / parallel conversion to obtain a parallel symbol vector s = (s0, s1, s2,..., s MN-1 ) T .

3. The method for designing OTFS waveforms based on a three-dimensional constellation mapper in a high-speed mobile scenario according to claim 2, characterized in that, In step S2, apply three-dimensional constellation mapping technology to perform constellation mapping on the parallel bits to obtain the mapped three-dimensional symbols, specifically: where x i , y i , z i , and i = 0, ..., MN - 1 are the three-dimensional coordinates of the constellation points in the Q-order three-dimensional constellation diagram.

4. The method for designing OTFS waveforms based on a three-dimensional constellation mapper in a high-speed mobile scenario according to claim 3, characterized in that, In step S3, perform I / Q transformation operation on the mapped three-dimensional symbols to convert them into I / Q complex symbols, specifically: where P is the number of complex signals in the I / Q matrix and P = (3 / 2) × MN, j is the imaginary unit and 5. The OTFS waveform design method based on a three-dimensional constellation mapper in a high-speed mobile scenario according to claim 4, wherein, In step S4, place the I / Q complex symbols in the delay-Doppler lattice and use zero-padding to generate the OTFS data block to be modulated, specifically: In the time-delay Doppler domain, there are M' time-delay grid points along the time-delay axis and N' Doppler grid points along the Doppler axis. Let the time-delay grid points and the Doppler grid points be equal, i.e., M' = N'. At this time, the OTFS data block becomes a square matrix, and let the dimension of this square matrix be where represents taking the integer upper bound. Among them, the grid points in the OTFS data block where complex signals are not placed are filled with zeros. After zero-padding, the matrix form of the OTFS data block is as follows: where s n,m is the complex signal vector in X I / Q , and the subscripts (n, m) of s n, n m represent the Doppler grid position and the delay grid position in the delay-Doppler grid, respectively.

6. The OTFS waveform design method based on a three-dimensional constellation mapper in a high-speed mobile scenario according to claim 5, wherein, In step S5, modulate the OTFS data block by OTFS, add CP, and send it into the extended vehicle signal for transmission, specifically: The OTFS data block can be expressed after inverse symplectic Fourier transform: X TF = F M' X DD F N' H where (.) H denotes conjugate transpose, then F N' H denotes the N'-point inverse Fourier transform matrix, and TF denotes the time-frequency domain; Convert the signal X in the time-frequency domain TF into the time-domain signal V through the inverse discrete Fourier transform: V = F M' H X TF Vectorize the time-domain signal V to obtain the signal v to be transmitted after modulation: v = vec(V) = vec(X DD F N' H ) Add CP to the signal after completing OTFS modulation and send it into the extended vehicle channel for transmission.

7. The OTFS waveform design method based on a three-dimensional constellation mapper in a high-speed mobile scenario according to claim 1, wherein, In step S7, the channel matrix formed by the complete channel state information obtained by the minimum mean square error detector through channel estimation is the equivalent channel matrix H in step S6. eff , and the estimated result of the time-delay Doppler domain symbol obtained after being detected by the minimum mean square error detector is:

8. The OTFS waveform design method based on a three-dimensional constellation mapper in a high-speed mobile scenario according to claim 1, wherein, The number of symbols for discarding 0 in step S8 is M'N' - MN.

9. The OTFS waveform design method based on a three-dimensional constellation mapper in a high-speed mobile scenario according to claim 1, wherein, In step S9, the complex signal of the I / Q two-way transmission estimated by the receiving end is converted into the three-dimensional symbol coordinates in the three-dimensional constellation diagram through a transformation matrix; in step S10, the minimum distance decision is used to demap the three-dimensional symbols into parallel bits; in step S11, the parallel bits after demapping are converted from parallel to serial to obtain the estimated value of the binary bit stream.

Images