A timing offset estimation method and system based on time domain super-nyquist signal and storage medium

Abstract

The application discloses a timing deviation estimation method and system based on a time-domain super-Nyquist signal and a storage medium in the field of information communication. The method comprises the following steps: acquiring a sending signal and sampling to generate a sample point sequence, and splicing the sample point sequence into a received signal vector; performing timing deviation estimation based on the received signal vector to obtain a parameter matrix containing timing deviation; performing equidistant discrete sampling on the offset time quantity in the parameter matrix to obtain a parameter matrix; initializing the parameter matrix and setting an initial timing deviation estimation value, a timing deviation threshold value, an initial error value and an iteration counter; in the iteration, it is judged whether the current error value exceeds the timing deviation threshold value, if yes, the error value and the timing deviation estimation value are updated; if no, the iteration is stopped, and the final timing deviation estimation value is output. The application can significantly reduce the influence of timing deviation on transmission performance, and has higher precision and robustness in the low signal-to-noise ratio and long symbol scenarios.

Description

Technical Field

[0001] This invention relates to a timing deviation estimation method, system, and storage medium based on time-domain super Nyquist signals, belonging to the field of information and communication technology. Background Technology

[0002] In wireless communication systems, timing error estimation is a crucial step in recovering the transmitted signal from the receiver. By estimating the timing error and adjusting the sampling clock, performance loss in the transmission system can be reduced. Currently, timing error estimation techniques are broadly classified into closed-loop and open-loop methods. Closed-loop techniques use the previously estimated error to control the timing adjustment loop, dynamically outputting the estimated value. For example, the early-late gate algorithm requires a sampling rate greater than twice the symbol rate, using the maximum likelihood function to determine the error magnitude and control the loop, bringing the error close to zero. The Gardener algorithm has a similar approach, but the sampling rate can be appropriately reduced. Open-loop techniques directly estimate the error value from the received data based on estimation criteria. For example, the squaring method uses Taylor series approximation to calculate the maximum likelihood function, while the AVN and LOGN methods use different approximation methods. However, the drawback of existing technologies is that traditional algorithms are designed for Nyquist signals, and there is a lack of relevant estimation algorithms for time-domain super-Nyquist signals. Summary of the Invention

[0003] The purpose of this invention is to provide a timing deviation estimation method, system, and storage medium based on time-domain super Nyquist signals. This invention can solve the limitation of traditional timing deviation estimation algorithms, which are designed for sub-Nyquist signals and cannot effectively handle time-domain super Nyquist signals. In particular, the existing methods suffer from low timing estimation accuracy and poor robustness in super Nyquist transmission scenarios due to inter-symbol interference and sampling deviation.

[0004] To solve the above-mentioned technical problems, the present invention is implemented using the following technical solution.

[0005] On one hand, the present invention provides a timing deviation estimation method based on time-domain super Nyquist signals, executed by a wireless channel receiver, comprising:

[0006] Acquire the transmitted signal;

[0007] The received transmitted signal is sampled to obtain a sample sequence, and the sample sequence is concatenated to obtain a received signal vector;

[0008] The received signal vector is subjected to timing deviation estimation to obtain a parameter matrix containing timing deviation;

[0009] The offset time values ​​in the parameter matrix are sampled at equal intervals to obtain a discrete parameter matrix;

[0010] The discrete parameter matrix is ​​initialized, and the initial timing deviation estimate, timing deviation threshold, initial error value, and iteration counter are set. The timing deviation objective function is constructed using the maximum likelihood criterion. The following operations are performed during each iteration:

[0011] Calculate the first and second derivatives of the timing deviation objective function;

[0012] The current error value is obtained based on the magnitude of the first derivative.

[0013] The iteration step size is determined by the first and second derivatives, and the timing deviation estimate is adjusted using the iteration step size, while the iteration counter is incremented.

[0014] Determine whether the current error value is greater than the timing deviation threshold. If the current error value is greater than the timing deviation threshold, continue iterating and update the current error value and the timing deviation estimate. If the current error value is not greater than the timing deviation threshold, stop iterating and output the final timing deviation estimate.

[0015] In conjunction with the first aspect, further, timing deviation estimation is performed on the received signal vector to obtain a parameter matrix containing timing deviation, including:

[0016] Discretization with equal intervals is performed using a shaping filter to obtain a discrete sample vector;

[0017] The discrete sample vectors are concatenated into a shaped filter matrix;

[0018] Based on the shaping filter matrix and the received signal vector, a parameter matrix containing timing bias is constructed.

[0019] In conjunction with the first aspect, the expression for the shaping filter matrix further includes:

[0020] ;

[0021] in, Indicates the offset time; L represents the sampling point length; Indicates the amount of time offset The discrete sample vector of the first shaping filter; Indicates the amount of time offset The discrete sample vector of the second shaping filter; Indicates the amount of time offset The Discrete sample vectors of a shaping filter; Indicates the amount of time offset The discrete sample vector of the Lth shaping filter; This represents the shaping filter matrix.

[0022] In conjunction with the first aspect, the expression for the parameter matrix containing the timing deviation further includes:

[0023] ;

[0024] Where s represents the received signal vector; This represents the conjugate transpose of the received signal vector s; Represents the shaping filter matrix; Represents the shaping filter matrix The conjugate transpose of ; Represents a parameter matrix containing timing bias; This indicates the amount of time offset.

[0025] In conjunction with the first aspect, further, the offset time quantities in the parameter matrix are sampled at equal intervals to obtain a discrete parameter matrix, including:

[0026] The offset time is divided into multiple equally spaced sampling points within a certain range;

[0027] Based on the offset time value corresponding to each sampling point, discrete parameter matrix values ​​are calculated, thereby constructing a discrete parameter matrix.

[0028] In conjunction with the first aspect, the expression for the discrete parameter matrix values ​​further includes:

[0029] ;

[0030] in, Represents a parameter matrix containing timing bias; Indicates the offset time; m represents the index value of the sampling point; M represents the total number of sampling points; Represents discrete parameter matrix values.

[0031] In conjunction with the first aspect, further, if the current error value is greater than the timing deviation threshold, the iteration continues, and the current error value and the timing deviation estimate are updated, including:

[0032] Calculate the timing deviation objective function first derivative and second derivative ;

[0033] The current timing deviation estimate Substituting the first and second derivatives, we obtain the first timing deviation value. Second timing deviation value ;

[0034] By calculating the first timing deviation value The modulus value is used to obtain the current error value (error).

[0035] According to the first timing deviation value Second timing deviation value The ratio of these values ​​yields the iteration step size;

[0036] The timing deviation estimate is updated using the iteration step size, the iteration count is incremented by one, the current error value is recalculated, and it is determined whether the iteration termination condition is met.

[0037] In conjunction with the first aspect, the expression for updating the timing bias estimate using the iterative step size further includes:

[0038] ;

[0039] in, This represents the estimated timing deviation for the (k+1)th time. This represents the estimated timing deviation for the kth time. This represents the step size set for each iteration; k represents the number of iterations.

[0040] Secondly, a timing deviation estimation system based on a time-domain super Nyquist signal includes:

[0041] At the receiving end:

[0042] The sampling and splicing module is used to sample the received transmitted signal to obtain a sample sequence, and splice the sample sequence to obtain a received signal vector;

[0043] The deviation estimation module is used to estimate the timing deviation of the received signal vector to obtain a parameter matrix containing the timing deviation.

[0044] The sampling module is used to sample the offset time values ​​in the parameter matrix at equal intervals to obtain a discrete parameter matrix.

[0045] The iterative loop module is used to initialize the discrete parameter matrix, set the initial timing deviation estimate, timing deviation threshold, initial error value, and iteration counter, and construct the timing deviation objective function using the maximum likelihood criterion. During each iteration, it performs the following operations:

[0046] Calculate the first and second derivatives of the timing deviation objective function;

[0047] The current error value is obtained based on the magnitude of the first derivative.

[0048] The iteration step size is determined by the first and second derivatives, and the timing deviation estimate is adjusted using the iteration step size, while the iteration counter is incremented.

[0049] Determine whether the current error value is greater than the timing deviation threshold. If the current error value is greater than the timing deviation threshold, continue iterating and update the current error value and the timing deviation estimate. If the current error value is not greater than the timing deviation threshold, stop iterating and output the final timing deviation estimate.

[0050] Thirdly, a computer-readable storage medium having a computer program stored thereon, characterized in that the program, when executed by a processor, implements the steps of the method described in the first aspect.

[0051] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0052] This invention acquires the transmitted signal and samples it to generate a sample point sequence, which is then concatenated to construct the received signal vector. Based on the conditional maximum likelihood criterion, the received signal vector is used to estimate the timing deviation, and a parameter matrix containing the offset time is derived. This parameter matrix is ​​discretized by sampling at equal intervals, and the initial estimated value, error threshold, and iteration counter are initialized. During the iteration process, it is dynamically determined whether the current error value exceeds the timing deviation threshold. If it does, the step size and estimated value are updated by calculating the first and second derivatives of the objective function until the error converges below the threshold, and finally, a high-precision timing deviation estimation result is output.

[0053] This method effectively overcomes the limitations of traditional algorithms caused by the design of sub-Nyquist signals through a conditional maximum likelihood iterative optimization mechanism, and significantly reduces the impact of inter-symbol interference and sampling deviation on timing estimation. Attached Figure Description

[0054] Figure 1 The diagram shows a flowchart of a timing deviation estimation method for time-domain super Nyquist signals provided in an embodiment of the present invention.

[0055] Figure 2 The diagram shown illustrates the transmission and reception process of a time-domain super Nyquist signal according to an embodiment of the present invention.

[0056] Figure 3 The figure shown is a timing deviation estimation performance curve provided by an embodiment of the present invention. Detailed Implementation

[0057] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0058] The term "and / or" simply describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. Additionally, the character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0059] Example 1

[0060] See Figure 1 This embodiment describes a timing deviation estimation method based on time-domain super Nyquist signals, which is executed by a wireless channel receiver and includes:

[0061] Step S1: Obtain the transmission signal;

[0062] At the receiving end, in order to successfully receive the transmitted signals, the buffer temporarily stores the received transmitted signals. After a sufficient number of transmitted signals have been accumulated, they are processed in batches. Meanwhile, the register is used to store relevant information such as the control parameters of the sampling clock, the initial value of the timing deviation estimate, and the number of iterations.

[0063] For example, suppose the receiver is a digital signal processing system whose hardware includes buffers and registers. During the initialization phase: the buffers are cleared, ready to receive new signal data; the parameters in the registers are set to initial values, such as the sampling clock frequency, the initial value of the timing deviation estimate, etc. These initialization operations ensure that the receiver is in the correct state when it starts receiving signals, enabling it to smoothly sample and process signals.

[0064] Step S2: Sample the received transmitted signal to obtain a sample sequence, and concatenate the sample sequence into a received signal vector s;

[0065] Here, the received signal vector s contains timing deviation, which causes the receiver to be unable to demodulate the transmitted signal normally. Therefore, timing deviation estimation needs to be performed at the receiving end, see step S3.

[0066] Step S3: Estimate the timing deviation of the received signal vector to obtain a parameter matrix containing the timing deviation;

[0067] The construction process of the parameter matrix containing timing bias includes:

[0068] Step S31: Use a shaping filter to perform equal-interval discretization to obtain a discrete sample vector;

[0069] Here, the receiving end needs to use the same shaping filter as the transmitting end to recover and process the signal in order to limit the signal bandwidth and reduce inter-symbol interference during signal transmission.

[0070] Step S32: Concatenate the discrete sample vectors into a shaped filter matrix;

[0071] The expression for the shaping filter matrix includes:

[0072] ;

[0073] in, Indicates the offset time; L represents the sampling point length; Indicates the amount of time offset The discrete sample vector of the first shaping filter; Indicates the amount of time offset The discrete sample vector of the second shaping filter; Indicates the amount of time offset The Discrete sample vectors of a shaping filter; Indicates the amount of time offset The discrete sample vector of the Lth shaping filter; This represents the shaping filter matrix.

[0074] The shaping filter matrix here It contains discrete sample information of the shaping filter under different offset time values, which provides a basis for subsequent timing bias estimation.

[0075] Step S33: According to the shaped filter matrix A parameter matrix containing timing bias is constructed using the received signal vector s.

[0076] By combining the received signal vector s with the correlation matrix of the shaping filter and performing matrix operations, a parameter matrix related to the timing deviation is obtained.

[0077] The expression for the parameter matrix containing timing bias includes:

[0078] ;

[0079] Where s represents the received signal vector; This represents the conjugate transpose of the received signal vector s; Represents the shaping filter matrix; Represents the shaping filter matrix The conjugate transpose of ; This represents a parameter matrix containing timing bias.

[0080] Step S4: Sample the offset time values ​​in the parameter matrix at equal intervals to obtain a discrete parameter matrix;

[0081] Constructed parameter matrix containing timing bias Offset time amount As a continuous-time variable, however, in practical digital signal processing, it is necessary to... Discretization is achieved by sampling the parameters at equal intervals. Specifically:

[0082] Step S41: Calculate the offset time amount Divide the sample into M equally spaced sampling points within a certain range;

[0083] Step S42: Based on the offset time amount corresponding to each sampling point The discrete parameter matrix values ​​are calculated, and thus a discrete parameter matrix is ​​constructed.

[0084] Here, the offset time value corresponding to each sampling point m is... Substitute the parameter matrix containing timing bias In this process, a discrete parameter matrix is ​​generated, the expression of which is:

[0085] ;

[0086] Where m represents the index value of the sampling point; M represents the total number of sampling points; Represents discrete parameter matrix values.

[0087] Step S5: Initialize the discrete parameter matrix and set the initial timing deviation estimate, timing deviation threshold, initial error value, and iteration counter;

[0088] Here, the initial timing deviation estimate is set to The timing deviation threshold is set to The initial error value is set to error=100 to ensure that the error value is much greater than the timing deviation threshold in the initial state. The initial iteration number is set to k=0 to determine whether the iteration has terminated.

[0089] The timing deviation objective function is constructed using the maximum likelihood criterion, and the following operations are performed during each iteration:

[0090] Calculate the first and second derivatives of the timing deviation objective function;

[0091] The current error value is calculated based on the magnitude of the first derivative.

[0092] The iteration step size is determined by the first and second derivatives, and the timing deviation estimate is adjusted using the iteration step size, while the iteration counter is incremented.

[0093] Determine whether the current error value is greater than the timing deviation threshold. If the current error value is greater than the timing deviation threshold, continue iterating and update the error value and the timing deviation estimate. If the current error value is not greater than the error threshold, stop iterating and output the final timing deviation estimate.

[0094] The execution process for each iteration includes the following steps:

[0095] Step S51: Construct the timing deviation objective function using the maximum likelihood criterion. As iterations continue, the first derivative of the timing deviation objective function is recalculated. and second derivative ;

[0096] Step S52: Estimate the current timing deviation value Substituting the first and second derivatives, we obtain the first timing deviation value. Second timing deviation value ;

[0097] Step S53: Obtain the current error value (error) by calculating the modulus of the first timing deviation value;

[0098] The expression for the current error value is:

[0099]

[0100] in, Indicates the error value; denoted by , which represents the first time deviation value, i.e., the first derivative of the current time deviation estimate; k represents the number of iterations.

[0101] Step S54: Calculate the iteration step size based on the ratio of the first timing deviation value to the second timing deviation value;

[0102] Here, the expression for the iteration step size after each loop is:

[0103]

[0104] in, This indicates the step size set for each iteration. This represents the second timing deviation value, which is the second derivative of the current timing deviation estimate.

[0105] Step S55: Update the timing deviation estimate using the iteration step size, increment the iteration count by one, recalculate the current error value, and determine whether the conditions for terminating the iteration are met.

[0106] The expression for updating the timing bias estimate using the iteration step size includes:

[0107]

[0108] in, This represents the estimated timing deviation for the (k+1)th time. This represents the estimated timing deviation value for the kth time.

[0109] Step S56: If the new error value is still greater than the timing deviation threshold, the timing deviation estimate has not yet reached the required accuracy, and steps S51 to S55 need to be repeated for the next iteration; otherwise, if the new error value is less than or equal to the timing deviation threshold, the iteration process is stopped, and the final timing deviation estimate is output as the result for subsequent signal processing steps, such as signal demodulation and recovery.

[0110] Example 2

[0111] Based on the same inventive concept as Embodiment 1, see [link to Embodiment 1] Figure 3 The performance differences between the proposed timing bias estimation algorithm based on conditional maximum likelihood and the traditional flat method were compared under different symbol lengths. The horizontal axis represents the symbol signal-to-noise ratio (Es / No), and the vertical axis represents the mean square error (MSE) of the normalized timing bias estimation. The symbol length N is 128, 512, and 1024, respectively.

[0112] The shaped waveform uses an energy-normalized root-raised cosine waveform, and the compression factor of the time-domain super Nyquist signal is set between 0 and 1. Results show that, for the same symbol length, the MSE of the proposed method is significantly lower than that of the flat method as the signal-to-noise ratio increases, especially in the low signal-to-noise ratio region. For example, when N=1024 and Es / No is 20dB, the MSE of the proposed scheme is approximately... The flat method only achieved The magnitude of the MSE decreases with increasing signal-to-noise ratio (SNR) (e.g., exceeding 40 dB). This is due to inter-symbol interference (ISI) introduced by time-domain super-Nyquist transmission. When the tail length of the shaping filter is sufficiently long, ISI can be approximated as Gaussian noise. Therefore, even if channel noise is further reduced, the timing deviation estimation performance cannot be improved by increasing the SNR. Furthermore, increasing the symbol length has a positive impact on both algorithms, but the proposed method shows a greater performance improvement with longer symbols (e.g., N=1024), indicating its superior robustness to data length compared to the traditional flat method. The curves in the figure also show that when N=128, the MSE difference between the proposed scheme and the flat method narrows after the SNR exceeds 30 dB, but its performance advantage remains consistent with high symbol lengths (N=1024), further validating the effectiveness of this method for timing deviation estimation of time-domain super-Nyquist signals.

[0113] Example 3

[0114] Based on the same inventive concept as Embodiment 1 and Embodiment 2, Figure 2 The process of transmitting and receiving time-domain super Nyquist signals is demonstrated. This invention is further described from a system-level perspective.

[0115] At the transmitting end, information bits are first converted into M-QAM modulation symbols by a symbol mapping module. These M-QAM modulation symbols then enter the FTN shaping filter module, where the shaping filter allows for moderate overlap between symbols, enabling higher symbol rates. The processed signal is then transmitted to the receiving end via the channel, during which it may be affected by noise such as additive white Gaussian noise.

[0116] Upon arrival at the receiving end, the signal needs to be sampled and converted into a discrete-time sample sequence. The accuracy of the sampling clock is crucial for signal recovery; timing deviations can cause sampling points to deviate from their optimal positions, introducing errors. To address this issue, the receiving end employs a timing deviation estimation algorithm based on the conditional maximum likelihood criterion. This algorithm estimates and corrects the timing deviation through an iterative process, outputting an accurate timing deviation estimate for subsequent signal processing, such as demodulation and recovery.

[0117] Specifically, the receiving end includes several key modules to achieve accurate timing deviation estimation, including:

[0118] The sampling and splicing module is used to sample the received transmitted signal to obtain a sample sequence, and splice the sample sequence into a received signal vector to provide a data basis for subsequent processing.

[0119] The deviation estimation module is used to estimate the timing deviation of the received signal vector to obtain a parameter matrix containing the timing deviation.

[0120] The sampling module is used to further sample the offset time values ​​in the parameter matrix at equal intervals to obtain a discrete parameter matrix, so as to facilitate subsequent digital processing and analysis.

[0121] The loop iteration module is the core part of the system. It is used to initialize the discrete parameter matrix and set key parameters such as the initial timing deviation estimate, timing deviation threshold, initial error value, and iteration counter.

[0122] The timing deviation objective function is constructed using the maximum likelihood criterion, and the following operations are performed during each iteration:

[0123] Calculate the first and second derivatives of the timing deviation objective function;

[0124] The current error value is obtained based on the magnitude of the first derivative.

[0125] The iteration step size is determined by the first and second derivatives, and the timing deviation estimate is adjusted using the iteration step size, while the iteration counter is incremented.

[0126] The system determines whether the current error value is greater than the timing deviation threshold. If the current error value is greater than the timing deviation threshold, the iteration continues, and the error value and timing deviation estimate are updated. If the current error value is not greater than the timing deviation threshold, the iteration stops, and the final timing deviation estimate is output. Through this iterative process based on the conditional maximum likelihood criterion, the system can achieve better timing deviation estimation performance than the traditional squaring method, thereby effectively reducing the negative impact of timing deviation on transmission performance and improving the overall stability and reliability of the communication system.

[0127] Example 4

[0128] A computer-readable storage medium having a computer program stored thereon, characterized in that the program, when executed by a processor, comprises the steps of the method described in any one of Embodiments 1 to 2.

[0129] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0130] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0131] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0132] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0133] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A timing deviation estimation method based on time-domain super Nyquist signals, characterized in that, Performed by the wireless channel receiver, including: Acquire the transmitted signal; The received transmitted signal is sampled to obtain a sample sequence, and the sample sequence is concatenated to obtain a received signal vector; The received signal vector is subjected to timing deviation estimation to obtain a parameter matrix containing timing deviation; The offset time values ​​in the parameter matrix are sampled at equal intervals to obtain a discrete parameter matrix; The discrete parameter matrix is ​​initialized, and the initial timing deviation estimate, timing deviation threshold, initial error value, and iteration counter are set. The timing deviation objective function is constructed using the maximum likelihood criterion. The following operations are performed during each iteration: Calculate the first and second derivatives of the timing deviation objective function; The current error value is obtained based on the magnitude of the first derivative. The iteration step size is determined by the first and second derivatives, and the timing deviation estimate is adjusted using the iteration step size, while the iteration counter is incremented. Determine whether the current error value is greater than the timing deviation threshold. If the current error value is greater than the timing deviation threshold, continue iterating and update the current error value and the timing deviation estimate. If the current error value is not greater than the timing deviation threshold, stop iterating and output the final timing deviation estimate.

2. The timing deviation estimation method based on time-domain super Nyquist signal according to claim 1, characterized in that, The received signal vector is subjected to timing deviation estimation to obtain a parameter matrix containing timing deviation, including: Discretization with equal intervals is performed using a shaping filter to obtain a discrete sample vector; The discrete sample vectors are concatenated into a shaped filter matrix; Based on the shaping filter matrix and the received signal vector, a parameter matrix containing timing bias is constructed.

3. The timing deviation estimation method based on time-domain super Nyquist signal according to claim 2, characterized in that, The expression for the shaping filter matrix includes: ； in, Indicates the offset time; L represents the sampling point length; Indicates the amount of time offset The discrete sample vector of the first shaping filter; Indicates the amount of time offset The discrete sample vector of the second shaping filter; Indicates the amount of time offset The Discrete sample vectors of a shaping filter; Indicates the amount of time offset The discrete sample vector of the Lth shaping filter; This represents the shaping filter matrix.

4. The timing deviation estimation method based on time-domain super Nyquist signal according to claim 2, characterized in that, The expression for the parameter matrix containing timing bias includes: ； Where s represents the received signal vector; This represents the conjugate transpose of the received signal vector s; Represents the shaping filter matrix; Represents the shaping filter matrix The conjugate transpose of ; Represents a parameter matrix containing timing bias; This indicates the amount of time offset.

5. The timing deviation estimation method based on time-domain super Nyquist signal according to claim 1, characterized in that, A discrete parameter matrix is ​​obtained by sampling the offset time values ​​in the parameter matrix at equal intervals, including: The offset time is divided into multiple equally spaced sampling points within a certain range; Based on the offset time value corresponding to each sampling point, discrete parameter matrix values ​​are calculated, thereby constructing a discrete parameter matrix.

6. The timing deviation estimation method based on time-domain super Nyquist signal according to claim 5, characterized in that, The expression for the discrete parameter matrix values ​​includes: ； in, Represents a parameter matrix containing timing bias; Indicates the offset time; m represents the index value of the sampling point; M represents the total number of sampling points; Represents discrete parameter matrix values.

7. The timing deviation estimation method based on time-domain super Nyquist signal according to claim 1, characterized in that, If the current error value is greater than the timing deviation threshold, the iteration continues, and the current error value and the estimated timing deviation value are updated, including: Calculate the timing deviation objective function first derivative and second derivative ; The current timing deviation estimate Substituting the first and second derivatives, we obtain the first timing deviation value. Second timing deviation value ; By calculating the first timing deviation value The modulus value is used to obtain the current error value (error). According to the first timing deviation value Second timing deviation value The ratio of these values ​​yields the iteration step size; The timing deviation estimate is updated using the iteration step size, the iteration count is incremented by one, the current error value is recalculated, and it is determined whether the iteration termination condition is met.

8. The timing deviation estimation method based on time-domain super Nyquist signal according to claim 7, characterized in that, The expression for updating the timing bias estimate using the iteration step size includes: ； in, This represents the estimated timing deviation for the (k+1)th time. This represents the estimated timing deviation for the kth time. This represents the step size set for each iteration; k represents the number of iterations.

9. A timing deviation estimation system based on time-domain super Nyquist signals, characterized in that, include: At the receiving end: The sampling and splicing module is used to sample the received transmitted signal to obtain a sample sequence, and splice the sample sequence to obtain a received signal vector; The deviation estimation module is used to estimate the timing deviation of the received signal vector to obtain a parameter matrix containing the timing deviation. The sampling module is used to sample the offset time values ​​in the parameter matrix at equal intervals to obtain a discrete parameter matrix. The iterative loop module is used to initialize the discrete parameter matrix, set the initial timing deviation estimate, timing deviation threshold, initial error value, and iteration counter, and construct the timing deviation objective function using the maximum likelihood criterion. During each iteration, it performs the following operations: Calculate the first and second derivatives of the timing deviation objective function; The current error value is obtained based on the magnitude of the first derivative. The iteration step size is determined by the first and second derivatives, and the timing deviation estimate is adjusted using the iteration step size, while the iteration counter is incremented. Determine whether the current error value is greater than the timing deviation threshold. If the current error value is greater than the timing deviation threshold, continue iterating and update the current error value and the timing deviation estimate. If the current error value is not greater than the timing deviation threshold, stop iterating and output the final timing deviation estimate.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method according to any one of claims 1 to 8.

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