Timing deviation estimation method and system based on time domain super-Nyquist signal, and storage medium

Abstract

The invention 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, sampling to generate a sampling point sequence, and splicing the sampling point sequence into a receiving signal vector; performing timing deviation estimation based on the received signal vector to obtain a parameter matrix containing timing deviation; performing equal-interval discretization sampling on the offset time quantity in the parameter matrix to obtain the parameter matrix; initializing a parameter matrix and setting an initial timing deviation estimation value, a timing deviation threshold value, an initial error value and an iteration counter; judging whether the current error value exceeds a timing deviation threshold value or not in iteration, and if so, updating the error value and the timing deviation estimation value; and if not, stopping iteration, and outputting a final timing deviation estimation value. According to the method, the influence of timing deviation on the transmission performance can be remarkably reduced, and higher precision and robustness are shown in a low signal-to-noise ratio and long symbol scene.

Description

Technical Field

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

[0002] In a wireless communication system, timing deviation estimation is an important link for the receiving end to recover the transmitted signal. By estimating the timing deviation and adjusting the sampling clock, the performance loss of the transmission system can be reduced. Currently, timing deviation estimation techniques are divided into two major categories: closed-loop and open-loop. Closed-loop techniques use the previous estimated deviation to control the timing adjustment loop and dynamically output the estimated value. For example, the early-late gate algorithm requires the sampling rate to be greater than twice the symbol rate, and uses the maximum likelihood function to judge the error size to control the loop, making the deviation approach zero; the Gardener algorithm has a similar idea, but the sampling rate can be appropriately reduced. Open-loop techniques directly estimate the deviation value from the received data according to the estimation criterion. For example, the squaring method uses Taylor series approximation to calculate the maximum likelihood function, and the AVN method and the LOGN method use different approximation methods. However, the defect of the existing technical solutions 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 the present invention is to provide a method, system and storage medium for timing deviation estimation based on time-domain super-Nyquist signals, which can solve the limitation problem that traditional timing deviation estimation algorithms cannot effectively process time-domain super-Nyquist signals because they are designed for sub-Nyquist signals, especially the technical defects of low timing estimation accuracy and poor robustness caused by inter-symbol interference and sampling deviation in the super-Nyquist transmission scenario of the existing methods.

[0004] To solve the above technical problems, the present invention is implemented by adopting the following technical solutions.

[0005] On the one hand, the present invention provides a method for timing deviation estimation based on time-domain super-Nyquist signals, which is executed by the receiving end of a wireless channel and includes: Obtain the transmitted signal; Sample the received transmitted signal to obtain a sample point sequence, and splice the sample point sequence to obtain a received signal vector; Estimate the timing deviation of the received signal vector to obtain a parameter matrix containing the timing deviation; Perform equally spaced sampling on the offset time amount in the parameter matrix to obtain a discrete parameter matrix; Initialize the discrete parameter matrix, and set the initial timing deviation estimation value, timing deviation threshold, initial error value and iteration counter, and construct a timing deviation objective function using the maximum likelihood criterion. In each iteration process, perform the following operations, including: Calculate the first - order derivative and the second - order derivative of the timing deviation objective function; Obtain the current error value according to the modulus value of the first - order derivative; Determine the iteration step size through the first - order derivative and the second - order derivative, adjust the timing deviation estimate value using the iteration step size, and increment the iteration counter; Judge 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 the iteration and update the current error value and the timing deviation estimate value; if the current error value is not greater than the timing deviation threshold, stop the iteration and output the final timing deviation estimate value.

[0006] Combined with the first aspect, further, performing timing deviation estimation on the received signal vector to obtain a parameter matrix containing timing deviation, including: Perform equally - spaced discretization using a shaping filter to obtain a discrete sample point vector; Concatenate the discrete sample point vectors into a shaping filter matrix; Construct a parameter matrix containing timing deviation according to the shaping filter matrix and the received signal vector.

[0007] Combined with the first aspect, further, the expression of the shaping filter matrix includes: ; where, represents the offset time amount; L represents the length of the sampling points; represents the discrete sample point vector of the first shaping filter containing the offset time amount ; represents the discrete sample point vector of the second shaping filter containing the offset time amount ; represents the discrete sample point vector of the th shaping filter containing the offset time amount ; represents the discrete sample point vector of the L - th shaping filter containing the offset time amount ; represents the shaping filter matrix.

[0008] Combined with the first aspect, further, the expression of the parameter matrix containing timing deviation includes: ; where, s represents the received signal vector; represents the conjugate transpose vector of the received signal vector s; represents the shaping filter matrix; represents the shaping filter matrix Conjugate transpose vector; Denote the parameter matrix with timing deviation; Denote the offset time amount.

[0009] Combined with the first aspect, further, equally spaced sampling is performed on the offset time amount in the parameter matrix to obtain a discrete parameter matrix, including: Divide the offset time amount into multiple equally spaced sampling points within a certain range; According to the offset time amount corresponding to each sampling point, calculate the discrete parameter matrix value, so as to construct a discrete parameter matrix.

[0010] Combined with the first aspect, further, the expression of the discrete parameter matrix value includes: ; Wherein, Denote the parameter matrix with timing deviation; Denote the offset time amount; m represents the index value of the sampling point; M represents the total number of sampling points; Denote the discrete parameter matrix value.

[0011] Combined with the first aspect, further, if the current error value is greater than the timing deviation threshold, continue to iterate, and update the current error value and the timing deviation estimate value, including: Calculate the first derivative of the timing deviation objective function and the second derivative ; Substitute the current timing deviation estimate value into the first derivative and the second derivative to obtain the first timing deviation value and the second timing deviation value ; By calculating the modulus value of the first timing deviation value , obtain the current error value error; According to the ratio of the first timing deviation value and the second timing deviation value , obtain the iteration step size; Use the iteration step size to update the timing deviation estimate value, increment the iteration count by one, and recalculate the current error value to determine whether the iteration termination condition is satisfied.

[0012] Combined with the first aspect, further, the expression for updating the timing deviation estimate value using the iteration step size includes: ; Wherein, It represents the (k + 1)-th timing deviation estimation value; It represents the k-th timing deviation estimation value; It represents the step size set for each loop iteration; k represents the number of iterations.

[0013] In a second aspect, a timing deviation estimation system based on a time-domain super-Nyquist signal includes: At the receiving end: A sampling and splicing module, configured to sample the received transmitted signal to obtain a sample point sequence, and splice the sample point sequence to obtain a received signal vector; A deviation estimation module, configured to perform timing deviation estimation on the received signal vector to obtain a parameter matrix containing timing deviation; A sampling module, configured to perform equally-spaced sampling on the offset time amount in the parameter matrix to obtain a discrete parameter matrix; A loop iteration module, configured to initialize the discrete parameter matrix, set an initial timing deviation estimation value, a timing deviation threshold, an initial error value, and an iteration counter, and construct a timing deviation objective function using the maximum likelihood criterion. In each iteration process, the following operations are performed, including: Calculate the first derivative and the second derivative of the timing deviation objective function; Obtain the current error value according to the modulus value of the first derivative; Determine the iteration step size through the first derivative and the second derivative, adjust the timing deviation estimation value using the iteration step size, and increment the iteration counter; Judge 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 the iteration and update the current error value and the timing deviation estimation value; if the current error value is not greater than the timing deviation threshold, stop the iteration and output the final timing deviation estimation value.

[0014] In a third aspect, a computer-readable storage medium stores a computer program, characterized in that when the program is executed by a processor, the steps of the method described in the first aspect are implemented.

[0015] Compared with the prior art, the beneficial effects achieved by the present invention: The present invention obtains a transmitted signal and samples it to generate a sequence of samples, thereby splicing and constructing a received signal vector; performs timing deviation estimation on the received signal vector based on the conditional maximum likelihood criterion, and derives a parameter matrix containing the offset time amount; discretizes the parameter matrix by equidistant sampling, and initializes the setting of an initial estimate value, an error threshold, and an iteration counter; dynamically determines during the iteration process whether the current error value exceeds the timing deviation threshold, and if it exceeds the limit, updates the step size and the estimate value by calculating the first derivative and the second derivative of the objective function until the error converges below the threshold, and finally outputs a high-precision timing deviation estimation result.

[0016] This method effectively overcomes the limitations caused by the design for sub-Nyquist signals in traditional algorithms through a conditional maximum likelihood iterative optimization mechanism, and significantly reduces the influence of inter-symbol interference and sampling deviation on timing estimation. Brief Description of the Drawings

[0017] Figure 1 The figure shows a flowchart of a method for estimating the timing deviation of a time-domain super-Nyquist signal provided by an embodiment of the present invention; Figure 2 The figure shows a diagram of the transmission and reception process of a time-domain super-Nyquist signal provided by an embodiment of the present invention; Figure 3 The figure shows a performance curve diagram of timing deviation estimation provided by an embodiment of the present invention. Detailed Embodiments

[0018] The technical solution of the present invention will be described in detail below with reference to the 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 on the technical solution of the present invention. Without conflict, the technical features in the embodiments of the present invention and the embodiments can be combined with each other.

[0019] The term "and / or" merely describes the associated relationship of the associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist simultaneously, and B exists alone. In addition, the character " / " generally represents an "or" relationship between the associated objects before and after.

[0020] Embodiment 1 Refer to Figure 1 , this embodiment introduces a method for estimating the timing deviation based on a time-domain super-Nyquist signal provided by the present invention, which is executed by the receiving end of a wireless channel, and includes: Step S1, obtain the transmitted signal; At the receiving end, in order to successfully receive the transmitted signal, the buffer temporarily stores the received transmitted signal. After accumulating enough transmitted signals, batch processing is performed. Meanwhile, the register is used to store relevant information such as control parameters of the sampling clock, initial values of timing deviation estimates, and the number of iterations.

[0021] For example: Assume that the receiving end is a digital signal processing system, and its hardware part includes a buffer and a register. In the initialization stage: The buffer is cleared to prepare for receiving new signal data; the parameters in the register are set to initial values, such as the frequency of the sampling clock, the initial value of the timing deviation estimate, etc. These initialization operations ensure that the receiving end is in the correct state when starting to receive signals and can smoothly perform signal sampling and subsequent processing.

[0022] Step S2: Sample the received transmitted signal to obtain a sample point sequence, and splice the sample point sequence into a received signal vector s; Here, there is a timing deviation in the received signal vector s, which causes the receiver to be unable to correctly demodulate the transmitted signal. Therefore, timing deviation estimation needs to be performed at the receiving end. Refer to step S3.

[0023] Step S3: Perform timing deviation estimation on the received signal vector to obtain a parameter matrix containing the timing deviation; The construction process of the parameter matrix containing the timing deviation includes: Step S31: Use the shaping filter for equally spaced discretization to obtain a discrete sample point vector; Here, the receiving end needs to use the same shaping filter as the transmitting end for signal recovery and processing in order to limit the signal bandwidth and reduce inter-symbol interference during signal transmission.

[0024] Step S32: Splice the discrete sample point vector into a shaping filter matrix; The expression of the shaping filter matrix, the expression of the shaping filter matrix, includes: ; Among them, represents the offset time amount; L represents the sampling point length; represents the discrete sample point vector of the first shaping filter containing the offset time amount ; represents the discrete sample point vector of the second shaping filter containing the offset time amount ; represents the discrete sample point vector of the th shaping filter containing the offset time amount ; represents the discrete sample point vector of the shaping filter containing the offset time amount The discrete sample vector of the L-th shaping filter; Represents the shaping filter matrix.

[0025] The shaping filter matrix here Contains the discrete sample information of the shaping filter at different offset time amounts, providing a basis for subsequent timing deviation estimation.

[0026] Step S33: According to the shaping filter matrix And the received signal vector s, construct a parameter matrix containing timing deviation.

[0027] By combining the received signal vector s with the correlation matrix of the shaping filter and performing matrix operations, a parameter matrix related to timing deviation is obtained.

[0028] The expression of the parameter matrix containing timing deviation includes: ; Where s represents the received signal vector; Represents the conjugate transpose vector of the received signal vector s; Represents the shaping filter matrix; Represents the shaping filter matrix Of the conjugate transpose vector; Represents the parameter matrix containing timing deviation.

[0029] Step S4: Perform equally spaced sampling on the offset time amount in the parameter matrix to obtain a discrete parameter matrix; The constructed parameter matrix containing timing deviation The offset time amount in Is a continuous time variable. However, in actual digital signal processing, it is necessary to Perform equally spaced sampling on the parameter to achieve discretization. Specifically: Step S41: Divide the offset time amount Into M equally spaced sampling points within a certain range; Step S42: According to the offset time amount corresponding to each sampling point , calculate the discrete parameter matrix values, thereby constructing a discrete parameter matrix.

[0030] Here, substitute the offset time amount Corresponding to each sampling point m into the parameter matrix containing timing deviation To generate a discrete parameter matrix. The expression of the discrete parameter matrix is: ; Where m represents the index value of the sampling point; M represents the total number of sampling points; Represents discrete parameter matrix values.

[0031] Step S5: Initialize the discrete parameter matrix, and set the initial timing deviation estimate value, timing deviation threshold, initial error value, and iteration counter; Here, the initial timing deviation estimate value is set to , the timing deviation threshold is set to , the initial error value error = 100 to ensure that the error value is much larger than the timing deviation threshold in the initial state, and the initial number of iterations k = 0 is used to determine whether the iteration terminates.

[0032] Among them, using the maximum likelihood criterion to construct the timing deviation objective function, the following operations are performed in each iteration process, including: Calculate the first derivative and second derivative of the timing deviation objective function; Calculate the current error value according to the modulus value of the first derivative; Determine the iteration step size through the first derivative and second derivative, and use the iteration step size to adjust the timing deviation estimate value and increment the iteration counter; Judge 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 the iteration and update the error value and the timing deviation estimate value; if the current error value is not greater than the error threshold, stop the iteration and output the final timing deviation estimate value.

[0033] Specifically, the execution process of each iteration includes the following steps: Step S51: Use the maximum likelihood criterion to construct the timing deviation objective function , when continuing the iteration, recalculate the first derivative and the second derivative ; Step S52: Substitute the current timing deviation estimate value into the first derivative and second derivative to obtain the first timing deviation value and the second timing deviation value ; Step S53: Obtain the current error value error by calculating the modulus value of the first timing deviation value; The expression of the current error value is:

[0034] Among them, represents the error value; represents the first timing deviation value, that is, the first derivative of the current timing deviation estimate value; k represents the number of iterations.

[0035] Step S54: Calculate the iteration step size according to the ratio of the first timing deviation value to the second timing deviation value. Here, the expression of the iteration step size after each loop is:

[0036] where represents the step size set for each loop iteration; represents the second timing deviation value, that is, the second derivative of the current timing deviation estimate value.

[0037] Step S55: Update the timing deviation estimate value using the iteration step size, increment the iteration count by one, and recalculate the current error value, and determine whether the condition for terminating the iteration is satisfied.

[0038] The expression for updating the timing deviation estimate value using the iteration step size includes:

[0039] where represents the (k + 1)-th timing deviation estimate value; represents the k-th timing deviation estimate value.

[0040] Step S56: If the new error value is still greater than the timing deviation threshold, it means that the timing deviation estimate value has not reached the required accuracy, and it is necessary to repeat steps S51 to S55 for the next iteration; otherwise, if the new error value is less than or equal to the timing deviation threshold, stop the iteration process, and use the final timing deviation estimate value as the result for output, which is used for subsequent signal processing steps, such as signal demodulation and recovery.

[0041] Embodiment 2 Based on the same inventive concept as in Embodiment 1, refer to Figure 3 , and compare the performance differences between the proposed timing deviation estimation algorithm based on conditional maximum likelihood and the traditional squaring method under different symbol lengths. The abscissa is the symbol signal-to-noise ratio (Es / No), and the ordinate is the mean square error (MSE) of the normalized timing deviation estimate. The symbol lengths N are taken as 128, 512, and 1024 respectively.

[0042] Among them, the shaping waveform adopts an energy-normalized root-raised cosine waveform, and the compression factor of the time-domain super-Nyquist signal is set between 0 and 1. The results show that, under the same symbol length, the MSE of the proposed method decreases significantly with the increase of the signal-to-noise ratio compared with the squaring method, especially in the low signal-to-noise ratio region. For example, when N = 1024 and Es / No = 20 dB, the MSE of the proposed scheme is about , while the squaring method only reaches Magnitude. As the signal-to-noise ratio is further increased (e.g., exceeding 40 dB), the MSE of both algorithms levels off and no longer decreases significantly. This is due to the inter-symbol interference introduced by time-domain super-Nyquist transmission. When the tail length of the shaping filter is long enough, the inter-symbol interference can be approximated as Gaussian noise. At this time, even if the channel noise is further reduced, the performance of timing deviation estimation cannot be improved by increasing the signal-to-noise ratio. In addition, the increase in symbol length has a positive impact on both algorithms, but the proposed method has a greater performance improvement under long symbols (such as N = 1024), indicating that its robustness to data length is better than that of the traditional squaring method. The curves in the figure also show that when N = 128, the gap between the MSE of the proposed scheme and the squaring method narrows after the signal-to-noise ratio exceeds 30 dB. However, at high symbol lengths (N = 1024), its performance advantage is always maintained, further verifying the effectiveness of this method for timing deviation estimation of time-domain super-Nyquist signals.

[0043] Embodiment 3

[0044] Based on the same inventive concept as in Embodiment 1 and Embodiment 2, Figure 2 The transmission and reception processes of time-domain super-Nyquist signals are shown, and the present invention further describes the invention from a system-level perspective.

[0045] At the transmitter, the information bits first pass through the symbol mapping module and are converted into M-QAM modulation symbols. The M-QAM modulation symbols then enter the FTN shaping filter module and are processed by the shaping filter, allowing moderate overlap between symbols to achieve higher symbol rate transmission. The processed signal is transmitted through the channel to the receiver, and during this process, it will be affected by noises such as additive white Gaussian noise.

[0046] After reaching the receiver, the signal needs to be sampled and converted into a discrete-time sample point sequence. The accuracy of the sampling clock is crucial for signal recovery. Timing deviation will cause the sampling points to deviate from the optimal positions and introduce errors. To solve this problem, the receiver adopts a timing deviation estimation algorithm based on the conditional maximum likelihood criterion, estimates and corrects the timing deviation through an iterative process, and outputs an accurate timing deviation estimation value for subsequent signal processing, such as signal demodulation and recovery.

[0047] Specifically, the receiver includes multiple key modules to achieve accurate timing deviation estimation, including: The sampling splicing module is used to sample the received transmitted signal to obtain a sample point sequence, and splice the sample point sequence into a received signal vector to provide a data basis for subsequent processing; 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; A sampling module, which is used to further perform equally-spaced sampling on the offset time amounts in the parameter matrix to obtain a discrete parameter matrix, so as to facilitate subsequent digital processing and analysis; The loop iteration module is the core part of the system and is used to initialize the discrete parameter matrix and set key parameters such as an initial timing deviation estimate value, a timing deviation threshold, an initial error value, and an iteration counter; Among them, a timing deviation objective function is constructed using the maximum likelihood criterion, and the following operations are performed in each iteration process, including: Calculate the first derivative and the second derivative of the timing deviation objective function; Obtain the current error value according to the modulus value of the first derivative; Determine the iteration step size through the first derivative and the second derivative, and use the iteration step size to adjust the timing deviation estimate value and increment the iteration counter; Judge 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 the iteration and update the error value and the timing deviation estimate value; if the current error value is not greater than the error threshold, stop the iteration and output the final timing deviation estimate value. Through this iterative process based on the conditional maximum likelihood criterion, the system can obtain better timing deviation estimation performance than the traditional squaring method, thereby effectively reducing the negative impact of timing deviation on the transmission performance and improving the overall stability and reliability of the communication system.

[0048] Embodiment 4

[0049] A computer-readable storage medium, on which a computer program is stored, characterized in that when the program is executed by a processor, the steps of the method according to any one of Embodiments 1 to 2 are implemented.

[0050] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.) containing computer-usable program codes.

[0051] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, and the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices produce a means for implementing the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks.

[0052] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory produce a manufactured article including an instruction means that implements the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks.

[0053] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks.

[0054] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many forms without departing from the spirit and scope protected by the present invention and the claims. All of these fall within the protection scope of the present invention.

Claims

1. A timing deviation estimation method based on time domain super-Nyquist signal, characterized in that: Executed by the wireless channel receiving end, including: Get the sending signal; Sampling the received transmission signal to obtain a sample point sequence, and concatenating the sample point sequence to obtain a received signal vector; Performing timing deviation estimation on the received signal vector to obtain a parameter matrix containing the timing deviation; The offset time quantities in the parameter matrix are sampled at equal intervals to obtain a discrete parameter matrix; Initialize the discrete parameter matrix, set an initial timing deviation estimate, a timing deviation threshold, an initial error value, and an iteration counter, and construct a timing deviation objective function using a maximum likelihood criterion. Perform the following operations in each iteration, including: Calculating the first-order derivative and the second-order derivative of the timing deviation objective function; Obtaining a current error value according to the modulus value of the first-order derivative; Determine an iteration step length by using the first-order derivative and the second-order derivative, adjust the timing deviation estimate value by using the iteration step length, and increment the iteration counter; 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 to iterate 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 iteration and output the final timing deviation estimate.

2. The timing deviation estimation method based on time domain super-Nyquist signal according to claim 1 is characterized in that: Performing timing deviation estimation on the received signal vector to obtain a parameter matrix containing the timing deviation includes: Using a shaping filter to discretize at equal intervals, a discrete sample vector is obtained; splicing the discrete sample point vectors into a shaped filter matrix; A parameter matrix containing timing deviation is constructed according to the shaping filter matrix and the received signal vector.

3. The timing deviation estimation method based on time domain super-Nyquist signal according to claim 2 is characterized in that: The expression of the shaping filter matrix includes: ； in, Indicates the offset time; L indicates the length of the sampling point; Indicates that the amount of time contains an offset The discrete sample vector of the first shaping filter; Indicates that the amount of time contains an offset The discrete sample vector of the second shaping filter; Indicates that the amount of time contains an offset No. A discrete sample vector of a shaping filter; Indicates that the amount of time contains an offset The discrete sample vector of the Lth shaping filter; represents the shaping filter matrix.

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

5. The timing deviation estimation method based on time domain super-Nyquist signal according to claim 1 is characterized in that: The offset time quantities in the parameter matrix are sampled at equal intervals to obtain a discrete parameter matrix, including: Dividing the offset time into a plurality of equally spaced sampling points within a certain range; According to the offset time amount corresponding to each sampling point, the discrete parameter matrix value is calculated, thereby constructing a discrete parameter matrix.

6. The timing deviation estimation method based on time domain super-Nyquist signal according to claim 5 is characterized in that: The expression of the discrete parameter matrix value includes: ； in, represents the parameter matrix containing the timing deviation; represents the offset time; m represents the index value of the sampling point; M represents the total number of sampling points; Represents the 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, continue to iterate and update the current error value and the timing deviation estimate, including: Calculate the timing deviation objective function The first derivative of and the second-order derivative ; The current timing deviation estimate Substituting the first-order derivative and the second-order derivative, the first timing deviation value is obtained. and the second timing deviation value ; By calculating the first timing deviation value The modulus value of , get the current error value error; According to the first timing deviation value and the second timing deviation value The ratio of , gets the iteration step length; The timing deviation estimation value is updated using the iteration step length, the number of iterations is increased by one, and the current error value is recalculated to determine 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 estimated value of the timing deviation using the iteration step size includes: ； in, represents the k+1th timing deviation estimate; represents the kth timing deviation estimate; Indicates the step size set for each loop iteration; k indicates the number of iterations.

9. A timing deviation estimation system based on time domain super-Nyquist signal, characterized in that: include: On the receiving end: A sampling and splicing module, used for sampling the received transmission signal to obtain a sample point sequence, and splicing the sample point sequence to obtain a received signal vector; A deviation estimation module, used to perform timing deviation estimation on the received signal vector to obtain a parameter matrix containing the timing deviation; A sampling module, used for sampling the offset time quantities in the parameter matrix at equal intervals to obtain a discrete parameter matrix; The loop iteration module is used to initialize the discrete parameter matrix, set the initial timing deviation estimate, the timing deviation threshold, the initial error value and the iteration counter, and construct the timing deviation objective function using the maximum likelihood criterion, and perform the following operations in each iteration process, including: Calculating the first-order derivative and the second-order derivative of the timing deviation objective function; Obtaining a current error value according to the modulus value of the first-order derivative; Determine an iteration step length by using the first-order derivative and the second-order derivative, adjust the timing deviation estimate value by using the iteration step length, and increment the iteration counter; 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 to iterate and update the current error value and the timing deviation estimate. If the current error value is not greater than the error threshold, stop iteration and output the final timing deviation estimate.

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

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