A CFO estimation method for LEO satellite communication system with Zak-OTFS modulation

Abstract

This invention proposes a CFO estimation method for LEO satellite communication systems using Zak-OTFS modulation, comprising: the transmitter mapping the data signal to the DD domain and setting pilot symbols in the DD domain; generating a time-domain transmit signal through discrete Zak inverse transform; the time-domain transmit signal being transmitted through the channel and superimposed with the CFO before reaching the receiver; the receiver performing a discrete Zak transform on the received signal to obtain the DD domain received signal and the DD domain input-output relationship; constructing a matching function related to the CFO based on the pilot symbols and the DD domain input-output relationship; calculating the matching function for each candidate within a preset CFO search set; and determining the CFO candidate that yields the optimal value of the matching function as the final estimation result. This invention utilizes the pilot structure and the input-output characteristics of the DD domain, effectively reducing computational complexity while ensuring high estimation accuracy, and avoiding the complex operations required in the time or TF domains by traditional CFO estimation algorithms.

Description

Technical Field

[0001] This invention relates to the field of satellite communication frequency synchronization, specifically to a CFO estimation method for LEO satellite communication systems using Zak-OTFS modulation. Background Technology

[0002] In high-speed mobile scenarios, such as low Earth orbit (LEO) satellite communication systems with orbital altitudes of 400–2000 km, links are susceptible to strong Doppler shifts and rapidly time-varying channels. Orthogonal Time Frequency Space (OTFS) modulation, a technique that modulates in the delay-Doppler (DD) domain, outperforms traditional Orthogonal Frequency Division Multiplexing (OFDM) modulation in highly mobile scenarios. The OTFS modulation framework was first proposed by Hadani et al., whose core idea is to map the signal to the DD domain to obtain an approximate time-invariant channel in highly mobile scenarios. Subsequently, Raviteja et al. further presented the input-output relationship in the DD domain and systematically analyzed the interference structure and detection methods, laying the foundation for OTFS receiver design.

[0003] In recent years, channel estimation, detection, and synchronization issues surrounding OTFS have gradually become research hotspots, with frequency synchronization being particularly critical. However, most existing OTFS modulation systems are based on OFDM (i.e., "OFDM-based OTFS" or Heisenberg-based OTFS). This structure employs a double modulation scheme on the transmitter side: first, information is mapped from the DD domain to the time-frequency (TF) domain using an inverse symplectic finite fourier transform (ISFFT); then, it is converted back to the time domain for transmission using an inverse fast fourier transform (IFFT). Although this structure is simple to implement and compatible with existing OFDM systems, it still relies on subcarrier orthogonality, and therefore inevitably suffers from carrier frequency offset (CFO) and Doppler coupling effects in high Doppler environments. On the one hand, frequency offset disrupts subcarrier orthogonality and introduces severe inter-carrier interference (ICI), complicating the synchronization and detection process. On the other hand, in LEO scenarios, the extremely high relative speed between satellites and users (up to 7.5 km / s) leads to a significant increase in normalized frequency offset. Traditional maximum likelihood estimation methods in the base TF domain or time-delay (TD) domain often face limitations in search range and a sharp increase in computational complexity, making it difficult to meet the real-time requirements of high-dynamic scenarios. In contrast, Zak-OTFS uses the Discrete Zak Transform (DZT) instead of the traditional OFDM structure, allowing the signal to be directly expanded in a two-dimensional block structure in the time-delay-Doppler domain, avoiding dependence on strict subcarrier orthogonality. This structural difference brings several important advantages: First, the Zak transform, through the combination of periodization and piecewise Fourier transform, makes the system more robust to CFO, thus significantly suppressing ICI diffusion effects similar to those in OFDM. Second, its mathematically good separability and quasi-periodic properties allow the CFO to exhibit a more regular structural expression in the DD domain, which is beneficial for establishing analytical models and designing low-complexity estimation algorithms. Furthermore, Zak-OTFS exhibits better stability when dealing with large-range frequency offsets, providing a new solution to synchronization problems in high Doppler scenarios.Therefore, based on the aforementioned research on OTFS frequency synchronization in OFDM, further exploring the CFO estimation and compensation method under the Zak-OTFS framework can not only effectively improve the robustness and accuracy of the system in the LEO satellite communication environment, but also help to deepen the understanding of the OTFS modulation mechanism, which has important theoretical significance and engineering application value. Summary of the Invention

[0004] To address the aforementioned problems, this invention proposes a CFO estimation method for LEO satellite communication systems using Zak-OTFS modulation. In LEO satellite communication scenarios with high-speed movement and large frequency offset, it achieves high-precision CFO estimation directly in the DD domain without going through the TF domain. It also ensures reliable signal recovery under different channel conditions while considering the computational complexity of the estimation algorithm, thereby improving the performance of the Zak-OTFS system in practical LEO satellite communication scenarios. The technical solution provided by this invention is as follows:

[0005] A method for estimating the CFO of a LEO satellite communication system using Zak-OTFS modulation includes the following steps:

[0006] The transmitter maps the data signal to the DD domain and sets pilot symbols in the DD domain. It then generates a time-domain transmit signal through discrete Zak inverse transform. The time-domain transmit signal is transmitted through the channel and superimposed with CFO before reaching the receiver.

[0007] The receiver performs a discrete Zak transform on the time-domain received signal to obtain the DD-domain received signal and the DD-domain input-output relationship.

[0008] Construct a matching function related to CFO based on pilot symbols and DD domain input-output relationships;

[0009] Calculate the matching function for each candidate within the preset CFO search set;

[0010] The CFO candidate that yields the optimal value for the matching function is determined as the final estimation result.

[0011] Preferably, the pilot symbol is set as a single pilot structure with a power higher than the data signal power, and the position of the pilot symbol is determined by... Characterization, in which Indicates the position of the time delay axis. Indicates the position of the Doppler axis, power is supplied by Characterization: When the channel conditions are typical multipath channels, a guard interval needs to be set to reduce multipath interference.

[0012] Preferably, the digital signal mapped to the DD domain is represented by a matrix. Characterization, , The number of time delay grid points, For Doppler points, each element is... Characterization;

[0013] For matrix Perform an inverse fast Fourier transform along the column direction on each row to obtain the matrix. ,matrix The elements in the middle are composed of Characterization, in which , ;

[0014] Then the matrix Straighten the columns to obtain the time-domain transmission signal. Each element is composed of Characterization, .

[0015] Preferably, when the channel is an ideal AWGN channel, the time-domain received signal expression at the receiver is as follows:

[0016]

[0017] in, It is the imaginary unit. It's a real CFO. It is additive white Gaussian noise; when the channel is a general multipath channel, the time-domain signal expression received by the receiver is as follows:

[0018]

[0019] in, It is the first Complex gain on each path Indicates the impact of channel delay. Indicates the channel Doppler effect, This indicates the influence of the CFO.

[0020] Preferably, the time-domain received signal is rearranged again into a format of size [missing value]. After obtaining the matrix, a Fast Fourier Transform (FFT) is performed on each row along the column direction to convert the time domain to the Doppler domain, thus obtaining the received signal matrix in the DD domain. If the channel is an ideal AWGN channel, the input-output relationship in the DD domain is as follows:

[0021]

[0022] If the channel is a typical multipath channel, then the input-output relationship in the DD domain is as follows:

[0023]

[0024] in, It is the Dirichlet kernel function. It is an additive white Gaussian noise representation in the DD domain.

[0025] Preferably, based on the input-output relationship in the DD domain, a least-squares cost matching function is constructed to estimate the CFO. If the channel is an ideal AWGN channel, the constructed least-squares cost matching function is expressed as follows:

[0026]

[0027] If the channel is a general multipath channel, then the constructed least-squares cost matching function is expressed as:

[0028]

[0029] in, It is a theoretical model of received signals. This indicates the complex conjugate operation.

[0030] Preferably, the variables in the least squares cost function Candidate CFO values ​​are taken from a predefined CFO search set and are represented as follows: ,in , For each candidate CFO value, calculate a matching function to match the size of the search set. or The CFO value corresponding to the maximum matching degree is selected as the final estimation result.

[0031] Compared with the prior art, the beneficial effects achieved by the present invention are:

[0032] This invention addresses LEO satellite communication systems employing Zak-OTFS modulation under high-speed mobility and large CFO conditions, considering various channel environments. Users construct a least-squares cost function and pre-set a CFO search set based on the input-output relationship in the DD domain to estimate the CFO. This method fully utilizes the pilot structure and the input-output characteristics of the DD domain, effectively reducing computational complexity while maintaining high estimation accuracy, avoiding the complex operations required in the time or TF domains by traditional CFO estimation algorithms. Furthermore, by analyzing the input-output relationship characteristics in the DD domain, a least-squares matching estimation function is constructed, significantly improving estimation accuracy and system robustness under large CFO conditions. Attached Figure Description

[0033] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0034] Figure 1 This is a flowchart of the CFO estimation method of the present invention;

[0035] Figure 2 The figure shows the simulation results of the CFO estimation method of the present invention compared with the RMSE of other methods under 16QAM modulation in an AWGN channel.

[0036] Figure 3 The figure shows the simulation results of the CFO estimation method of the present invention under 16QAM modulation in NTN-TDL-A multipath channel, comparing the RMSE with other methods.

[0037] Figure 4 The figure shows the simulation results of the CFO estimation method of the present invention under 16QAM modulation in NTN-TDL-A multipath channel, comparing the BER with other methods.

[0038] Figure 5 This is a comparison of the BER of the CFO estimation method of the present invention under different processing methods in AWGN channel QAM modulation of different orders;

[0039] Figure 6 The graph shows the BER comparison of the CFO estimation method of the present invention under different processing methods of QAM modulation of different orders in NTN-TDL-A multipath channel.

[0040] Figure 7 This is a comparison chart of BER for the CFO estimation method of the present invention under different M / N conditions. Detailed Implementation

[0041] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0042] To make the above-mentioned objectives, features and effects of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0043] Example 1: A CFO estimation method for a LEO satellite communication system using Zak-OTFS modulation, such as... Figure 1 As shown, it includes the following steps:

[0044] The transmitter maps the data signal to the DD domain and sets pilot symbols in the DD domain, generating a time-domain transmission signal through discrete Zak inverse transform;

[0045] The time-domain transmitted signal is transmitted through a channel (including both AWGN channels and general multipath channels) and superimposed with CFO before reaching the receiving end;

[0046] The receiving end performs a discrete Zak transform on the received signal to obtain the DD domain received signal and the DD domain input-output relationship.

[0047] Construct a matching function related to CFO based on pilot symbols and DD domain input-output relationships;

[0048] Within the pre-defined CFO search set, the matching function is calculated for each candidate frequency offset;

[0049] The CFO candidate that yields the optimal value for the matching function is determined as the final estimation result.

[0050] In practice, the user constructs an estimation function in the DD domain based on the pilot settings in the DD domain and the input-output relationship of the DD domain signal in the LEO satellite communication system, and obtains the CFO estimate using the least squares criterion. In the LEO satellite system, both the satellite and the ground user are equipped with only a single antenna, and the user has prior knowledge of the channel state information. In OTFS modulation, the number of delay grid points and the number of Doppler grid points are respectively... and The subcarrier spacing is The duration of an OFDM frame is CFOs are all based on Doppler intervals The normalized value; where the actual CFO uses This indicates that the candidate CFO value is... express( , (Depending on the size of the search set), the final estimated CFO is obtained using express.

[0051] The DD domain pilot is configured as a single pilot structure. By setting the pilot symbol power higher than the data signal power, the impact of data interference on CFO estimation is reduced. The pilot positions are determined by... Characterization, pilot signal power is determined by Characterization shows that if the channel conditions are ideal AWGN channels, there is no need to set a guard interval to improve spectrum efficiency; if the channel conditions are general multipath channels, a certain guard interval needs to be set to reduce multipath interference.

[0052] The data signal is mapped onto the DD domain grid, by Characterization ( ), where each element is composed of Characterization. Transmitted signal matrix in the DD domain. Perform an inverse fast Fourier transform along the column direction on each row to obtain the matrix. , Each element in the middle can be derived from Characterization, in which, , Then... Straighten the columns to obtain the time-domain transmitted signal vector. Each element is composed of Characterization, .matrix and vector The correspondence between the elements in the formula can be reflected by the following formula:

[0053]

[0054] The time-domain transmitted signal reaches the receiver through the channel, resulting in a time-domain received signal. Due to differences in channel conditions, the received signal will also vary. If the channel is an ideal AWGN channel, the expression for the time-domain signal received by the receiver is as follows:

[0055]

[0056] in, It is additive white Gaussian noise. If the channel is a general multipath channel, the channel in the DD domain can be represented as:

[0057]

[0058] in, It is the Dirac delta function. , and They are the first Complex gain, time delay, and Doppler shift along the path. and They are defined as follows:

[0059]

[0060] The time-domain signal received by the receiver is expressed as follows:

[0061]

[0062] in, It is due to channel delay. It's due to channel Doppler effect. It's due to the CFO's influence.

[0063] The above time-domain received signal is rearranged again into a value of... After obtaining the matrix, a Fast Fourier Transform (FFT) is performed on each row along the column direction. This FFT transforms the time domain to the Doppler domain, thus obtaining the received signal matrix in the DD domain. Two cases are discussed below:

[0064] If the channel is an ideal AWGN channel, then the DD domain input-output relationship is as follows:

[0065]

[0066] If the channel is a typical multipath channel, then the DD domain input-output relationship is as follows:

[0067]

[0068] in, It is the Dirichlet kernel function. It is an additive white Gaussian noise representation in the DD domain.

[0069] Based on the above DD domain input-output relationship, a least-squares cost matching function can be constructed to estimate the CFO. If the channel is an ideal AWGN channel, the constructed least-squares cost matching function can be expressed as:

[0070]

[0071] If the channel is a general multipath channel, then the constructed least-squares cost matching function can be expressed as:

[0072]

[0073] in, It is a theoretical model of received signals. This indicates the complex conjugate operation.

[0074] The variables in the above least squares cost function Taken from the preset CFO search set Calculate a matching function for each candidate CFO value. The CFO value corresponding to the maximum matching degree is selected as the final estimation result, i.e.:

[0075] Under ideal AWGN channel conditions, the CFO estimation result is as follows:

[0076]

[0077] Under typical multipath channel conditions, the CFO estimation result is as follows:

[0078]

[0079] To verify the beneficial effects of this invention, scientific demonstration was conducted through simulation experiments. The following is in conjunction with… Figures 2-7 The present invention will be further described in detail below:

[0080] Figure 2 and Figure 3This paper presents a comparison of the RMSE performance of three methods—the PDEKF algorithm, the step-by-step estimation method, and the LS-based estimation method proposed in this invention—at a signal-to-noise ratio (SNR) of 20 dB. The results show that the channel environment significantly affects CFO estimation. Under AWGN channels, all algorithms exhibit low RMSEs that do not change significantly with CFO, with the proposed method showing the best performance (approximately 10 dB). -4 The order of magnitude of the data is 1 / 3, with stepwise estimation being the next best and PDEKF being the worst. This is because in an AWGN environment, LS can fully utilize the observation data to achieve the optimal fit.

[0081] In the NTN-TDL-A channel, the overall RMSE is improved by about an order of magnitude, but the multipath effect significantly increases the estimation difficulty. The PDEKF method shows the most significant performance degradation, while the step-by-step estimation method has some robustness. The LS method, on the other hand, remains the best, demonstrating strong resistance to channel mismatch.

[0082] Figure 4 This paper presents the BER performance of different estimation methods under NTN-TDL-A channel conditions, with M=128, N=16, and an elevation angle of 85°, at a normalized CFO of 9.33. Overall, as the SNR increases from 0 dB to 20 dB, the BER of all three methods decreases significantly, indicating that noise has a significant impact on system performance. In the low SNR region (0~6 dB), the performance differences among the methods are small, but the method proposed in this invention shows the best performance, while PDEKF is the worst, indicating that it is more sensitive to noise. As the SNR increases (above 10 dB), the performance gap gradually widens, with the method proposed in this invention showing the fastest decline, reaching approximately 10 dB at 20 dB. -3 The order of magnitude is: firstly, step-by-step estimation is the next best, with relatively stable performance but error accumulation; PDEKF is consistently the worst.

[0083] Furthermore, in the high SNR region, performance differences are primarily determined by the accuracy of CFO estimation rather than noise. Overall, the LS method offers the best accuracy and robustness, while step-by-step estimation achieves a trade-off between complexity and performance, whereas PDEKF is more suitable for dynamic tracking but has weaker static performance.

[0084] Figure 5 and Figure 6The BER versus SNR curves for three processing methods (uncompensated, LS-estimated compensation, and ideal compensation) under different modulation schemes (4QAM and 16QAM) are presented under AWGN and NTN-TDL-A channel conditions, with M=128, N=16, and an elevation angle of 85° (normalized CFO of 9.33). Overall, modulation order, CFO compensation, and SNR jointly determine OTFS performance. 4QAM is generally superior to 16QAM, while the uncompensated scheme experiences performance saturation due to frequency offset interference. Compensation using the CFO estimated by the method of this invention significantly reduces BER and continues to improve with increasing SNR, but there is an error floor; ideal compensation offers the best performance.

[0085] Figure 7 This paper demonstrates the relationship between the BER (Best Per Count) and SNR (Simultaneous Range) of the OTFS-LEO system under different parameter configurations, with an AWGN channel and 16QAM modulation, at a satellite altitude of 400 km and an elevation angle of 85°. The four curves correspond to different combinations of delay dimension parameter M and Doppler dimension parameter N: N=16, M=128; N=64, M=128; N=64, M=16; and N=128, M=16. Overall, as the SNR increases, the BER of all curves continuously decreases, and the system performance gradually improves. In the low SNR region (0–8 dB), the curves are relatively close, with a BER of approximately 10. -1 This indicates that noise plays a dominant role.

[0086] When the SNR exceeds 10 dB, performance differences gradually become apparent. The worst performance is observed with N=16 and M=128, while the best performance is observed with N=128 and M=16. This indicates that increasing the Doppler dimension parameter N significantly improves performance and is beneficial for characterizing and compensating for frequency offset and Doppler spread. In contrast, the time delay dimension parameter M has a smaller impact, and the difference is not significant at the same level. In the high SNR region (18–20 dB), all curves rapidly decrease to 10 dB. -5 Even 10 -6 This further illustrates that increasing N helps the system enter the low error rate zone earlier, thereby improving communication reliability.

[0087] Example 2: The computer-readable storage medium of this example stores a computer program that, when executed by a processor, implements the steps in the CFO estimation method for a LEO satellite communication system using Zak-OTFS modulation in Example 1.

[0088] The computer-readable storage medium in this embodiment can be an internal storage unit of the terminal, such as the terminal's hard disk or memory; the computer-readable storage medium in this embodiment can also be an external storage device of the terminal, such as a plug-in hard disk, smart memory card, secure digital card, flash memory card, etc. equipped on the terminal; furthermore, the computer-readable storage medium can include both the terminal's internal storage unit and external storage devices.

[0089] The computer-readable storage medium of this embodiment is used to store computer programs and other programs and data required by the terminal. The computer-readable storage medium can also be used to temporarily store data that has been output or will be output.

[0090] Example 3: The computer device of this example includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the CFO estimation method of a LEO satellite communication system using Zak-OTFS modulation in Example 1.

[0091] In this embodiment, the processor can be a central processing unit, or other general-purpose processors, digital signal processors, application-specific integrated circuits, off-the-shelf programmable gate arrays or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc. The memory can include read-only memory and random access memory, and provides instructions and data to the processor. A portion of the memory can also include non-volatile random access memory. For example, the memory can also store device type information.

[0092] Those skilled in the art will clearly understand that each implementation can be achieved using software plus the necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0093] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A CFO estimation method for LEO satellite communication system with Zak-OTFS modulation, characterized in that, Includes the following steps: The transmitter maps the data signal to the DD domain and sets pilot symbols in the DD domain. It then generates a time-domain transmit signal through discrete Zak inverse transform. The time-domain transmit signal is transmitted through the channel and superimposed with CFO before reaching the receiver. The receiver performs a discrete Zak transform on the time-domain received signal to obtain the DD-domain received signal and the DD-domain input-output relationship. Construct a matching function related to CFO based on pilot symbols and DD domain input-output relationships; Calculate the matching function for each candidate within the preset CFO search set; The CFO candidate that yields the optimal value for the matching function is determined as the final estimation result.

2. The CFO estimation method for a LEO satellite communication system using Zak-OTFS modulation according to claim 1, characterized in that, The pilot symbols are set to a single pilot structure with a power higher than the data signal power. The position of the pilot symbols is determined by... Characterization, in which Indicates the position of the time delay axis. Indicates the position of the Doppler axis, power is supplied by Characterization: When the channel conditions are typical multipath channels, a guard interval needs to be set to reduce multipath interference.

3. The CFO estimation method for a LEO satellite communication system using Zak-OTFS modulation according to claim 2, characterized in that, The digital signal mapped to the DD domain is given by the matrix characterized by, , is the number of delay grid points, is the number of Doppler grid points, where each element is characterized by . ;​​​​​​ Again, the matrix is column-wise flattened to obtain the time-domain transmit signal where each element is represented by , .

4. The CFO estimation method for LEO satellite communication system with Zak-OTFS modulation according to claim 3, characterized in that, When the channel is an ideal AWGN channel, the time-domain received signal expression at the receiver is as follows: ； in, It is the imaginary unit. It's a real CFO. It is additive white Gaussian noise; when the channel is a general multipath channel, the time-domain signal expression received by the receiver is as follows: ； in, It is the first Complex gain on each path Indicates the impact of channel delay. Indicates the channel Doppler effect, This indicates the influence of the CFO.

5. The CFO estimation method for a LEO satellite communication system using Zak-OTFS modulation according to claim 4, characterized in that, The time-domain received signal is rearranged again to a value of... After obtaining the matrix, a Fast Fourier Transform (FFT) is performed on each row along the column direction to convert the time domain to the Doppler domain, thus obtaining the received signal matrix in the DD domain. If the channel is an ideal AWGN channel, the input-output relationship in the DD domain is as follows: ； If the channel is a typical multipath channel, then the input-output relationship in the DD domain is as follows: ； wherein is a Dirichlet kernel function, is an additive white Gaussian noise representation of the DD domain.

6. The CFO estimation method for a LEO satellite communication system using Zak-OTFS modulation according to claim 5, characterized in that, Based on the input-output relationship in the DD domain, a least-squares cost matching function is constructed to estimate the CFO. If the channel is an ideal AWGN channel, the constructed least-squares cost matching function is expressed as: ； If the channel is a general multipath channel, then the constructed least-squares cost matching function is expressed as: ； wherein is a theoretical received signal model, denotes a take complex conjugate operation.

7. The CFO estimation method for a LEO satellite communication system using Zak-OTFS modulation according to claim 6, characterized in that, Variables in the least squares cost function Candidate CFO values ​​are taken from a predefined CFO search set and are represented as follows: ,in , For each candidate CFO value, calculate a matching function to match the size of the search set. or The CFO value corresponding to the maximum matching degree is selected as the final estimation result.

8. A computer-readable storage medium having stored thereon a computer program, characterized in that, When the program is executed by the processor, it implements the steps in the CFO estimation method for a LEO satellite communication system using Zak-OTFS modulation as described in any one of claims 1-7.

9. A computer device comprising a processor, a memory and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the CFO estimation method for a LEO satellite communication system using Zak-OTFS modulation as described in any one of claims 1-7.

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