OTFS synaesthesia integrated PAPR suppression method based on virtual subcarrier

Abstract

The present invention discloses a method for suppressing the PAPR of an OTFS-synaesthesia integrated signal based on a virtual subcarrier. The method comprises the following steps: searching for the optimal reserved virtual subcarrier position; converting the OTFS-synaesthesia integrated signal into a time domain signal; calculating a signal threshold; outputting the time domain signal if the amplitude of the time domain signal is less than or equal to the signal threshold; otherwise, reducing the amplitude of the time domain signal; subtracting the amplitude-reduced time domain signal from the original signal to generate a shear noise signal; scaling the shear noise signal to obtain a scaling vector; updating the peak-reduced OTFS-synaesthesia integrated signal; terminating the algorithm and outputting the suppressed PAPR of the OTFS-synaesthesia integrated signal if the amplitude of the peak-reduced OTFS-synaesthesia integrated signal is less than or equal to the signal threshold or reaches a maximum number of iterations; otherwise, continuing to reduce the amplitude of the time domain signal. The present invention rapidly suppresses the PAPR of the OTFS-synaesthesia integrated signal, achieving a convergence state, and improving system stability.

Description

Technical Field

[0001] The present invention belongs to the technical field of synaesthesia integration and relates to an OTFS synaesthesia integration PAPR suppression method based on a virtual subcarrier. Background Art

[0002] With the increasing convergence of radar and communication systems in architecture and signal processing, integrated sensing and communication technologies are crucial to the development of sixth-generation mobile networks (6G). Since Hadani proposed a modulation scheme based on Orthogonal Time-Frequency Space (OTFS) in 2017, OTFS has garnered widespread attention in integrated sensing and communication technologies due to its excellent performance in dual-selective channels. Furthermore, the OTFS synaesthesia signal waveform has shown great promise in the field of ISACs. As a new two-dimensional modulation technique, however, as a multi-carrier modulation technique, the OTFS synaesthesia signal inevitably suffers from a high peak-to-average power ratio (PAPR), which results in efficiency loss and significant power reduction in high-power amplifiers.

[0003] Rose Mary Augustine of the Department of Electrical and Telecommunications Engineering at the Indian Institute of Science first derived the upper bound of the PAPR of the OTFS synaesthesia integrated signal and found that it To mitigate the PAPR problem, several techniques have been explored, which can be divided into three categories: pre-distortion techniques, coding techniques, and probabilistic techniques. Pre-distortion techniques usually reduce the amplitude of the signal, which can lead to a significant degradation in system performance. The ability of compression technology to reduce the PAPR of OTFS synaesthesia-integrated signals depends on the degree of signal distortion. Wang Zhenduo of Harbin Engineering University proposed a nonlinear corrected active constellation expansion method that uses a parametric compression transform to process peak-reduced signals, achieving significant PAPR reduction while maintaining good bit error rate (BER) performance.

[0004] Furthermore, coding techniques typically optimize some codewords to minimize the signal's PAPR. For example, Liu Mengxue of Zhejiang University proposed an autoencoder architecture leveraging deep learning, while Wang Zhenduo of Harbin Engineering University introduced a precoded OTFS synaesthesia integrated signal system based on an integral-weighted fractional Fourier transform. Both achieve a trade-off between PAPR and BER performance at the expense of high computational complexity at the receiver. In contrast, these techniques introduce additional distortion and noise to the integrated signal, making them less adaptable and flexible in practical applications. Summary of the Invention

[0005] The present invention aims to solve the technical problem that the distortion of the integrated signal affects the stability of the system. The present invention provides an OTFS synaesthesia integrated PAPR suppression method based on virtual subcarriers, and the technical solution adopted is:

[0006] The OTFS synaesthesia integrated PAPR suppression method based on virtual subcarriers includes the following steps:

[0007] S1. Searching for the best reserved virtual subcarrier position;

[0008] S2. Generate an OTFS synaesthesia integrated signal at a virtual subcarrier position outside the position of the optimal reserved virtual subcarrier, transform the OTFS synaesthesia integrated signal from the delay-Doppler domain to the virtual subcarrier domain, and convert it from the virtual subcarrier domain to a time domain signal;

[0009] S3. Calculating a signal threshold based on the average amplitude of the time domain signal; if the amplitude of the time domain signal is less than or equal to the signal threshold, outputting the time domain signal; otherwise, recording the amplitude of the time domain signal that exceeds the signal threshold, and proceeding to the next step;

[0010] S4, reducing the amplitude of the time domain signal exceeding the signal threshold, and subtracting the time domain signal with the reduced amplitude from the original signal to generate a shear noise signal;

[0011] S5. Scaling the shear noise signal to obtain a scaling vector;

[0012] S6. updating a peak-reduced OTFS synaesthesia integrated signal according to the shear noise signal and the scaling vector;

[0013] S7. If the amplitude of the peak-reduced OTFS-synaesthesia integrated signal is less than or equal to the signal threshold or the maximum number of iterations is reached, terminate the algorithm and output the peak-reduced OTFS-synaesthesia integrated signal to obtain the PAPR of the suppressed OTFS-synaesthesia integrated signal; otherwise, go to step S3.

[0014] Beneficial effects of the present invention:

[0015] The OTFS synaesthesia integrated signal PAPR suppression method of the present invention can accurately reduce the signal at the peak, thereby quickly suppressing the PAPR of the synaesthesia integrated signal based on OTFS modulation, and can quickly achieve a convergence effect without going through multiple iterations. Moreover, since the OTFS synaesthesia integrated signal can adapt to high-dynamic environments, and the location of the peak clipping signal formed by the method of the present invention is at the reserved virtual subcarrier, the data subcarrier is not changed, and therefore, the signal is not distorted and the communication bit error rate of the signal is not affected, so it is relatively stable. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 Flowchart of the OTFS synaesthesia integrated PAPR suppression method based on virtual subcarriers provided by an embodiment of the present invention;

[0017] Figure 2 2. This is a CCDF curve diagram of the PAPR of the OTFS synaesthesia integrated signal suppressed by the VTR algorithm provided by an embodiment of the present invention;

[0018] Figure 3 2. This is a comparison diagram of CCDF curves of different algorithms for suppressing the PAPR of OTFS synaesthesia integrated signals provided by an embodiment of the present invention;

[0019] Figure 4 This is a comparison chart of the bit error rate results of OTFS synaesthesia integrated signal communication under different algorithms provided by the embodiments of the present invention. DETAILED DESCRIPTION

[0020] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] Inspired by the tone reservation (TR) method, this paper proposes a peak-to-average power ratio (PAPR) suppression algorithm for orthogonal time-frequency space (OTFS) systems, called virtual tone reservation (VTR). This method uses virtual tone reservation to suppress the PAPR of OTFS synaesthesia integrated signals, achieving efficient PAPR suppression without signal distortion.

[0022] Refer to the attached Figure 1 The OTFS synaesthesia integrated PAPR suppression method based on virtual subcarrier of the present invention comprises the following steps:

[0023] S1. Searching for the best reserved virtual subcarrier position;

[0024] S2. generating an OTFS synaesthesia integrated signal at a virtual subcarrier position outside the position of the optimal reserved virtual subcarrier, transforming the OTFS synaesthesia integrated signal from the delay-Doppler domain to the virtual subcarrier domain, and converting the OTFS synaesthesia integrated signal from the virtual subcarrier domain to a time domain signal;

[0025] S3. Calculate the signal threshold based on the average amplitude of the time domain signal. If the amplitude of the time domain signal is less than or equal to the signal threshold, output the time domain signal. Otherwise, record the amplitude of the time domain signal that exceeds the signal threshold and proceed to the next step.

[0026] S4, reducing the amplitude of the time domain signal exceeding the signal threshold, and subtracting the time domain signal with the reduced amplitude from the original signal to generate a shear noise signal;

[0027] S5. Scaling the shear noise signal to obtain a scaling vector;

[0028] S6, updating the peak-reduced OTFS synaesthesia integration signal according to the sheared noise signal and the scaling vector;

[0029] S7. If the amplitude of the peak-reduced OTFS-synaesthesia integrated signal is less than or equal to the signal threshold or the maximum number of iterations is reached, terminate the algorithm and output the peak-reduced OTFS-synaesthesia integrated signal to obtain the PAPR of the suppressed OTFS-synaesthesia integrated signal; otherwise, go to step S3.

[0030] The present invention first converts a Delay-Doppler (DD) domain grid into virtual data subcarriers and virtual reserved subcarriers, and converts the two-dimensional data grid into a one-dimensional data grid. The virtual data subcarriers are used to carry radar and communication data, and the virtual reserved subcarriers are used to carry the generated peak-clipped signals. The optimal reserved virtual subcarrier position is then selected using a Firefly Algorithm (FA). The generated peak-reduced OTFS (on-the-fly synaesthesia) integrated signal is then updated using a gradient algorithm (Signal to Clipping Noise Ratio, SCR). This achieves the effect of rapidly suppressing the PAPR of the OTFS-modulated integrated signal, while efficiently reducing the PAPR of the integrated signal without distorting it.

[0031] Step S1 of the present invention comprises:

[0032] The optimal reserved virtual subcarrier position is expressed as:

[0033] (1);

[0034] In formula (1), To reserve the best virtual subcarrier position, Indicates the number of subcarriers, Indicates the number of symbols, represents the virtual subcarrier, OTFS synaesthesia integration is dimension, converted into reserved virtual subcarriers dimension, represents transpose, represents the first virtual subcarrier, Indicates the virtual subcarriers; It is the secondary peak of the best reserved virtual subcarrier, and the secondary peak is used to evaluate the performance of the selected best reserved virtual subcarrier.

[0035] The optimization of reserved virtual subcarriers is an NP-hard problem. In one embodiment of the present invention, a firefly algorithm (FA) is used to search for the best position of reserved virtual subcarriers.

[0036] FA is a nature-inspired metaheuristic algorithm suitable for solving heuristic search problems. Based on the flashing characteristics and mutual attraction of fireflies, FA is governed by two rules: First, all fireflies are attracted to other fireflies, regardless of their sex. Second, mutual attraction is proportional to brightness and decreases as the distance between fireflies increases. Furthermore, the brightness of a firefly represents a landscape of fitness values.

[0037] Each virtual frequency domain core is defined as a firefly, and is randomly generated with the number of reserved virtual subcarriers as a constraint. The brightness of a firefly is determined by the secondary peak of the time domain kernel.

[0038] The attraction between any two fireflies is expressed as:

[0039] (2);

[0040] In formula (2), is the attraction between any two fireflies, For maximum attraction, is the brightness attenuation coefficient, is the Euclidean distance between fireflies, is the index.

[0041] If the The brightness of the first firefly is greater than the The brightness of the firefly, The firefly will be attracted to the There are only fireflies nearby. The positions of the fireflies will be changed, represented by:

[0042] (3);

[0043] In formula (3), is the step length, For interval A random vector that follows a uniform distribution on Indicates the The location of the fireflies, Indicates the The location of the fireflies.

[0044] Update the brightness of the fireflies, sort the updated brightness of the fireflies again, repeat the operation until the maximum number of iterations set by yourself is reached, and output the current global optimal reserved virtual subcarrier.

[0045] In one embodiment of the present invention, step S2 includes:

[0046] For the OTFS synaesthesia integrated signal, the information symbols in the delay-Doppler domain are converted into time domain signals through inverse sigmoid Fourier transform and Heisenberg transform. The time domain signal of the OTFS synaesthesia integrated signal is expressed as:

[0047] (4);

[0048] In formula (4), represents the conjugate transpose operation, is the identity matrix, represents the Kronecker product, , represents column-by-column vectorization, represents the information symbol in the delay-Doppler domain, ISFFT represents the inverse sigmoid Fourier transform, HT represents the Heisenberg transform, represents the time domain signal, , express dimensional matrix, is the unit diagonal matrix, express Point IDFT matrix, express Point discrete Fourier transform matrix, express The point-wise inverse discrete Fourier transform matrix, is the number of subcarriers, is the number of symbols, Represents the communication data of OTFS synaesthesia integration in the delay-Doppler domain.

[0049] Let the middle vector , formula (4) is expressed as:

[0050] (5);

[0051] The OTFS synaesthesia integration signal that needs to reduce PAPR is obtained.

[0052] First, there are several combinations when creating a blank virtual subcarrier. At this time, the position you want to reserve is set to 1, and the data part is set to 0. After searching, a combination with the most concentrated peaks is found as the position of the reserved virtual subcarrier. Then, radar and communication data are generated. The data in the reserved position is 0. In order to carry the peak clipping signal generated later, the unreserved position carries radar and communication data. This constitutes a length of Integration of OTFS synaesthesia signals.

[0053] The optimal reserved virtual subcarrier position is 0, which is used to carry the subsequently generated peak-clipped signal. Virtual subcarrier positions outside the reserved position are used to carry radar and communication data. This is equivalent to adding the two signals to form an OTFS integrated signal with low PAPR.

[0054] Compared with Orthogonal Frequency Division Multiplexing (OFDM), it is worth noting that the OTFS modulation in formula (5) is very similar to OFDM modulation, where It can be regarded as having Virtual subcarrier parallel data streams can use a specific transformation matrix Convert it into an OTFS synaesthesia integrated signal that needs to reduce PAPR From this perspective, the PAPR reduction methods widely used in OFDM systems, such as the TR method, can achieve the expected PAPR performance without causing signal distortion and can be used to suppress the PAPR of the OTFS synaesthesia integrated signal. This is why a new PAPR reduction method is proposed: an OTFS synaesthesia integrated PAPR suppression method based on virtual subcarriers.

[0055] In one embodiment of the present invention, step S3 includes:

[0056] The signal threshold is expressed as:

[0057] (6);

[0058] In formula (6), is the signal threshold, The crop ratio is set by yourself. is the average amplitude of the time domain signal, Indicates the The amplitude of the time domain signal at the iteration, Indicates the The amplitude of the time domain signal at the iteration, Indicates the number of subcarriers, Indicates the number of symbols.

[0059] After obtaining the signal threshold, the amplitude of the time domain signal at this time is compared with the signal threshold. If the amplitude of the time domain signal is less than or equal to the signal threshold, enter step S7 and directly output the time domain signal. Otherwise, record the position where the amplitude of the time domain signal is greater than the signal threshold, and then proceed to step S4.

[0060] In one embodiment of the present invention, step S4 includes:

[0061] The shear noise signal is expressed as:

[0062] (7);

[0063] In formula (7), Indicates the The noise signal is cut at the iteration, represents the signal threshold, Indicates the The phase of the time domain signal obtained at the iteration, Represents the imaginary part; Combined with the position where the amplitude of the time domain signal is greater than the signal threshold, the signal at that position is Operation is performed to generate a peak clipping signal, reduce the amplitude of the time domain signal, and keep the phase of the time domain signal unchanged. The position where the amplitude of the time domain signal is less than or equal to the signal threshold is not processed, that is, a shearing noise signal is generated.

[0064] In one embodiment of the present invention, step S5 includes:

[0065] The scaling vector is expressed as:

[0066] (8);

[0067] In formula (8), Indicates the first The scaling value at the position is used to suppress the PAPR of the synaesthesia integration signal more quickly. Indicates the The peak value in the signal at iteration , is the proportional factor obtained when solving using the least squares method;

[0068] The scaling factor is expressed as:

[0069] (9);

[0070] In formula (9), is the set of peak positions, Indicates the The peak clipping signal generated at the iteration is For the The noise signal is clipped at the iteration.

[0071] In one embodiment of the present invention, step S6 includes:

[0072] The peak-reduced OTFS synaesthesia integration signal is expressed as:

[0073] (10);

[0074] In formula (10), Indicates the The peak value of the OTFS synaesthesia integration signal is reduced at the iteration time. represents the scaling vector, represents the signal threshold, Indicates the The phase of the time domain signal obtained at the iteration, , Indicates the number of subcarriers, Indicates the number of symbols, represents the imaginary part, Indicates the The peak value in the signal at iteration , P represents a virtual subcarrier, Indicates the The time domain signal at the iteration time.

[0075] In one embodiment of the present invention, step S7 includes:

[0076] The relationship between the amplitude of the peak-reduced OTFS-synaesthesia integrated signal and the signal threshold is determined. If the amplitude of the peak-reduced OTFS-synaesthesia integrated signal is less than or equal to the signal threshold or the number of iterations reaches a self-set maximum number of iterations, the algorithm is terminated and the peak-reduced OTFS-synaesthesia integrated signal is output to obtain the PAPR of the suppressed OTFS-synaesthesia integrated signal. Otherwise, the algorithm returns to step S3 to continue reducing the amplitude of the peak-reduced OTFS-synaesthesia integrated signal.

[0077] The PAPR of the OTFS synaesthesia integrated signal is expressed as:

[0078] (11);

[0079] In formula (11), represents the average power of the signal, Indicates the average, represents the discrete OTFS synaesthesia integration signal, Indicates the number of subcarriers, Indicates the number of symbols, Represents the PAPR of the OTFS synaesthesia integration signal.

[0080] The PAPR of the OTFS synaesthesia integration signal is measured using the complementary cumulative distribution function, which represents the probability that the PAPR crosses a predetermined peak power threshold and is expressed as;

[0081] (12);

[0082] In formula (12), CCDF represents the complementary cumulative distribution function, is the predetermined peak power threshold, express probability.

[0083] As with the TR technique, in formula (5) Virtual subcarriers can be divided into data virtual subcarriers and reserved virtual subcarriers. Data virtual subcarriers carry radar and communication data, while reserved virtual subcarriers generate clipped signals. The present invention first searches for the locations of reserved virtual subcarriers. Then, a scaling-SCR algorithm is used to generate clipped signals that effectively reduce PAPR.

[0084] The peak-reduced OTFS synaesthesia integrated signal consists of a time domain signal and a peak-clipped signal, which can be expressed as:

[0085] (13);

[0086] In formula (13), Indicates the OTFS synaesthesia integration signal after reducing PAPR, Indicates the need to reduce the PAPR of the OTFS synaesthesia integration signal, represents the peak clipping signal in the time domain, The symbol vector is reserved for the virtual frequency domain, ;

[0087] Since the virtual data subcarriers and the virtual reserved subcarriers are disjoint, the reserved symbol vector satisfy:

[0088] (14);

[0089] In formula (14), , and are respectively the positions of the virtual subcarriers outside the position of the best reserved virtual subcarrier and the position set of the best reserved virtual subcarrier, represents the virtual data subcarrier, A virtual reserved subcarrier, used to carry the generated peak clipping signal;

[0090] After applying the virtual subcarrier reservation method, the PAPR of the peak-reduced OTFS synaesthesia integrated signal is obtained, which is expressed as:

[0091] (15);

[0092] In formula (15), represents the average power of the signal, represents the discrete OTFS synaesthesia integration signal, Indicates peak clipping signal;

[0093] Peak reduction of OTFS synaesthesia integration signal Iterative update using the gradient algorithm is expressed as:

[0094] (16);

[0095] In formula (16), represents a one-dimensional scaling vector, , represents the signal threshold, is the cropping ratio, is the time domain kernel, For the The next iteration will The sequence is cyclically shifted to the peak position , is a virtual frequency domain kernel, satisfying .

[0096] In summary, the virtual subcarrier-based OTFS-synaesthesia integrated PAPR suppression method primarily incorporates two algorithms: a firefly algorithm for searching for the optimal reserved virtual subcarrier location, and a gradient-based VTR algorithm for PAPR reduction. This method eliminates signal distortion and thus reduces the communication bit error rate (BER), thereby improving the stability of the integrated system. Furthermore, it rapidly suppresses the PAPR of the OTFS-modulated synaesthesia integrated signal and allows it to converge quickly.

[0097] The effects of the present invention are further illustrated below through simulation.

[0098] 1. Simulation conditions:

[0099] The simulation of the present invention is carried out under the software environment of MATLAB R2022a.

[0100] 2. Simulation content:

[0101] In the experimental simulation, set the number of subcarriers is 128, the number of symbols If is 64, the total number of virtual tones is 8192. The number of virtual peak reduction tones (PRTs) is set to 320, as this typically accounts for 3% to 5% of the total tones. Quadrature Phase Shift Keying (QPSK) is used for modulation, and the remaining simulation parameters are shown in Table 1.

[0102] Table 1 Simulation parameters

[0103]

[0104] 3. Simulation effect analysis:

[0105] The simulation results are shown in the attached Figure 2 , by the attached Figure 2 It can be seen that when When the PAPR of the original signal is 12.75dB, after one iteration, the PAPR is 3.9dB, which is suppressed by 8.85dB; after two iterations, the PAPR is 3.2dB, which is suppressed by 9.55dB; after three iterations, the PAPR is 3.02dB, which is suppressed by 9.73dB; after four iterations, the PAPR is 3.0dB, which is suppressed by 9.75dB, which can achieve good suppression effect.

[0106] It can be seen from the simulation result graph that many peaks can be eliminated in the first iteration, and then gradually decrease. The third and fourth iterations basically tend to converge, which can achieve good PAPR suppression effect.

[0107] Attachment Figure 3 The performance of PAPR reduction under different methods is shown. Original signal (Original), VTR method, The PAPR reduction values ​​of the law compression method, CF method and PTS method are 8.8, 8.2, 7.4 and 6.6dB respectively. The results show that all methods can significantly reduce PAPR, but the VTR method is better than other methods.

[0108] Attachment Figure 4 Intuitively displays the original signal (Original), The OTFS system's bit error rate performance is reduced by methods such as compression, partial transmission sequence (PTS), and clipping factor (CF). This is because all three methods introduce signal distortion, thereby reducing bit error rate performance. In contrast, the VTR method of the present invention maintains the same bit error rate (BER) as the original signal. The results demonstrate that the VTR method of the present invention achieves PAPR reduction without introducing signal distortion. Therefore, the VTR method proposed in the present invention outperforms the other three methods.

[0109] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with this technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered by the scope of protection of the present invention.

Claims

1. The OTFS synaesthesia integrated PAPR suppression method based on virtual subcarrier is characterized by: Including steps: S1. Searching for the best reserved virtual subcarrier position; S2. Generate an OTFS synaesthesia integrated signal at a virtual subcarrier position outside the position of the optimal reserved virtual subcarrier, transform the OTFS synaesthesia integrated signal from the delay-Doppler domain to the virtual subcarrier domain, and convert it from the virtual subcarrier domain to a time domain signal; S3. Calculating a signal threshold based on the average amplitude of the time domain signal; if the amplitude of the time domain signal is less than or equal to the signal threshold, outputting the time domain signal; otherwise, recording the amplitude of the time domain signal that exceeds the signal threshold, and proceeding to the next step; S4. Reduce the amplitude of the time domain signal exceeding the signal threshold, and subtract the time domain signal with the reduced amplitude from the original signal to generate a shear noise signal; the shear noise signal is expressed as: (7)； In formula (7), Indicates the The noise signal is cut at the iteration, represents the signal threshold, Indicates the The phase of the time domain signal obtained at the iteration, represents the imaginary part; Combined with the position where the amplitude of the time domain signal is greater than the signal threshold, the signal at the position is Operation, generating a peak clipping signal, reducing the amplitude of the time domain signal, and keeping the phase of the time domain signal unchanged, and not processing the position where the amplitude of the time domain signal is less than or equal to the signal threshold, that is, generating the shearing noise signal; S5. Scaling the shear noise signal to obtain a scaling vector; S6. Update the peak-reduced OTFS-synaesthesia integrated signal according to the shear noise signal and the scaling vector; the peak-reduced OTFS-synaesthesia integrated signal is expressed as: (10)； In formula (10), Indicates the The peak value of the OTFS synaesthesia integration signal is reduced at the iteration time. represents the scaling vector, represents the signal threshold, Indicates the The phase of the time domain signal obtained at the iteration, , Indicates the number of subcarriers, Indicates the number of symbols, represents the imaginary part, Indicates the The peak value in the signal at iteration , P represents a virtual subcarrier, Indicates the Time domain signal at the iteration time; S7. If the amplitude of the peak-reduced OTFS-synaesthesia integrated signal is less than or equal to the signal threshold or the maximum number of iterations is reached, terminate the algorithm and output the peak-reduced OTFS-synaesthesia integrated signal to obtain the PAPR of the suppressed OTFS-synaesthesia integrated signal; otherwise, go to step S3.

2. The OTFS synaesthesia integrated PAPR suppression method based on virtual subcarrier according to claim 1 is characterized in that: The step S1 comprises: The position of the optimal reserved virtual subcarrier is expressed as: (1)； In formula (1), To reserve the best virtual subcarrier position, Indicates the number of subcarriers, Indicates the number of symbols, represents the virtual subcarrier, OTFS synaesthesia integration is dimension, converted into reserved virtual subcarriers dimension, represents transpose, represents the first virtual subcarrier, Indicates the virtual subcarriers; It is the secondary peak of the best reserved virtual subcarrier, and the secondary peak is used to evaluate the performance of the selected best reserved virtual subcarrier.

3. The OTFS synaesthesia integrated PAPR suppression method based on virtual subcarrier according to claim 1 is characterized in that: The step S2 comprises: For the OTFS synaesthesia integrated signal, the information symbols in the delay-Doppler domain are converted into time domain signals through inverse sigmoid Fourier transform and Heisenberg transform. The time domain signal of the OTFS synaesthesia integrated signal is expressed as: (4)； In formula (4), represents the conjugate transpose operation, is the identity matrix, represents the Kronecker product, , represents column-by-column vectorization, represents the information symbol in the delay-Doppler domain, ISFFT represents the inverse sigmoid Fourier transform, HT represents the Heisenberg transform, represents the time domain signal, , express dimensional matrix, is the unit diagonal matrix, express Point IDFT matrix, express Point discrete Fourier transform matrix, express The point-wise inverse discrete Fourier transform matrix, is the number of subcarriers, is the number of symbols, It represents the communication data of OTFS synaesthesia integration in the delay-Doppler domain; Let the middle vector , formula (4) is expressed as: (5)； The OTFS synaesthesia integration signal that needs to reduce PAPR is obtained.

4. The OTFS synaesthesia integrated PAPR suppression method based on virtual subcarrier according to claim 1, characterized in that: The step S3 comprises: The signal threshold is expressed as: (6)； In formula (6), is the signal threshold, The crop ratio is set by yourself. is the average amplitude of the time domain signal, Indicates the The amplitude of the time domain signal at the iteration, Indicates the The amplitude of the time domain signal at the iteration, Indicates the number of subcarriers, Indicates the number of symbols; After obtaining the signal threshold, the amplitude of the time domain signal at this time is compared with the signal threshold. If the amplitude of the time domain signal is less than or equal to the signal threshold, enter step S7 and directly output the time domain signal. Otherwise, record the position where the amplitude of the time domain signal is greater than the signal threshold, and then perform step S4.

5. The OTFS synaesthesia integrated PAPR suppression method based on virtual subcarrier according to claim 1, characterized in that: The step S5 comprises: The scaling vector is expressed as: (8)； In formula (8), Indicates the first The scaling value at the position is used to suppress the PAPR of the synaesthesia integration signal more quickly. Indicates the The peak value in the signal at iteration , is the proportional factor obtained when solving using the least squares method; The scaling factor is expressed as: (9)； In formula (9), is the set of peak positions, Indicates the The peak clipping signal generated at the iteration is For the The noise signal is clipped at the iteration.

6. The OTFS synaesthesia integrated PAPR suppression method based on virtual subcarrier according to claim 1, characterized in that: The step S7 comprises: Determine the relationship between the amplitude of the peak-reduced OTFS-synaesthesia integrated signal and the signal threshold; if the amplitude of the peak-reduced OTFS-synaesthesia integrated signal is less than or equal to the signal threshold or the number of iterations reaches a self-set maximum number of iterations, terminate the algorithm and output the peak-reduced OTFS-synaesthesia integrated signal to obtain the PAPR of the suppressed OTFS-synaesthesia integrated signal; otherwise, return to step S3 to continue reducing the amplitude of the peak-reduced OTFS-synaesthesia integrated signal; The PAPR of the OTFS synaesthesia integration signal is expressed as: (11)； In formula (11), represents the average power of the signal, Indicates the average, represents the discrete OTFS synaesthesia integration signal, Indicates the number of subcarriers, Indicates the number of symbols, Represents the PAPR of the OTFS synaesthesia integration signal.

7. The OTFS synaesthesia integrated PAPR suppression method based on virtual subcarrier according to claim 6, characterized in that: The PAPR of the OTFS synaesthesia integrated signal is measured using the complementary cumulative distribution function, which represents the probability that the PAPR crosses a predetermined peak power threshold, expressed as; (12)； In formula (12), CCDF represents the complementary cumulative distribution function, is the predetermined peak power threshold, express probability.

8. The OTFS synaesthesia integrated PAPR suppression method based on virtual subcarrier according to claim 7, characterized in that: The peak-reduced OTFS synaesthesia integrated signal consists of a time domain signal and a peak clipping signal, and is expressed as: (13)； In formula (13), Indicates the OTFS synaesthesia integration signal after reducing PAPR, Indicates the need to reduce the PAPR of the OTFS synaesthesia integration signal, represents the peak clipping signal in the time domain, The symbol vector is reserved for the virtual frequency domain, ; Since the virtual data subcarriers and the virtual reserved subcarriers are disjoint, the reserved symbol vector satisfy: (14)； In formula (14), , and are respectively the positions of the virtual subcarriers outside the position of the best reserved virtual subcarrier and the position set of the best reserved virtual subcarrier, represents the virtual data subcarrier, A virtual reserved subcarrier, used to carry the generated peak clipping signal; After applying the virtual subcarrier reservation method, the PAPR of the OTFS synaesthesia integrated signal with reduced peak value is obtained, which is expressed as: (15)； In formula (15), represents the average power of the signal, represents the discrete OTFS synaesthesia integration signal, Indicates peak clipping signal; Peak reduction of OTFS synaesthesia integration signal Iterative update using the gradient algorithm is expressed as: (16)； In formula (16), represents a one-dimensional scaling vector, , represents the signal threshold, is the cropping ratio, is the time domain kernel, For the The next iteration will The sequence is cyclically shifted to the peak position , is a virtual frequency domain kernel, satisfying .

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