A Gardner timing synchronization method, device and medium based on an optimized interpolation filter

Abstract

The application provides a Gardner timing synchronization method and device based on an optimized interpolation filter and a medium, the method comprising: initializing a Gardner timing synchronization loop based on a digital phase-locked loop; taking a linear weighted least mean square error as an objective function, establishing a linear constraint relationship according to a time domain interpolation constraint of an interpolation filter, performing constraint optimization iteration under a given signal bandwidth and image rejection frequency band condition, solving optimal interpolation filter tap coefficients, and making an actual frequency domain response approximate to an ideal frequency domain response; and implementing the optimal coefficients in a Farrow structure and embedding the optimal coefficients into the Gardner timing synchronization loop to complete recovery of an optimal sampling time under the driving of a fractional interval update. The application can effectively reduce interpolation error and timing jitter and improve synchronization robustness.

Description

Technical Field

[0001] This invention relates to the field of baseband signal processing technology for high-speed data transmission receivers in satellite communication, and specifically designs a Gardner timing synchronization method, device, and medium based on an optimized interpolation filter. Background Technology

[0002] In high-speed satellite data transmission, due to the high symbol rate, the receiver often needs to complete symbol timing recovery at a high processing rate. If the timing synchronization accuracy is insufficient when there are few sampling points, the symbol sampling will deviate from the optimal time, which will lead to a decrease in demodulation performance.

[0003] Existing timing synchronization methods often employ polynomial interpolation (such as linear interpolation, piecewise parabolic interpolation, cubic interpolation, etc.) to obtain fractional interval sampling points. While these methods can achieve timing recovery under certain conditions, they still have the following shortcomings: First, the interpolation filter coefficients of traditional interpolation methods are usually fixed values, making it difficult to flexibly adjust them according to actual transmission conditions and bandwidth requirements. Second, in complex scenarios such as high-order modulation, traditional interpolation may result in insufficient timing synchronization accuracy and a high bit error rate.

[0004] Therefore, there is an urgent need for a Gardner timing synchronization method that can improve timing synchronization accuracy through optimizable interpolation filter coefficients under conditions of high-speed data transmission and fewer sampling points, and is easy to implement in engineering. Summary of the Invention

[0005] This application provides a Gardner timing synchronization method, device, and medium based on an optimized interpolation filter to solve the problems of fixed interpolation coefficients, difficulty in adapting to different experimental / transmission conditions, and insufficient timing synchronization accuracy under high-order modulation in traditional high-speed data transmission systems.

[0006] Other features and advantages of this application will become apparent from the following detailed description, or may be learned in part from practice of this application.

[0007] According to a first aspect of the embodiments of this application, a Gardner timing synchronization method based on an optimized interpolation filter is provided, comprising: Initialize the Gardner timing synchronization loop based on a digital phase-locked loop; Using the linear weighted minimum mean square error as the objective function, a linear constraint relationship is established based on the time-domain interpolation constraint of the interpolation filter. Under the given signal bandwidth and image suppression frequency band, constraint optimization iteration is performed to solve for the optimal interpolation filter tap coefficients, so that the actual frequency domain response approximates the ideal frequency domain response. The optimal coefficients are implemented using a Farrow structure and embedded in the Gardner timing synchronization loop, and the optimal sampling time is recovered under the drive of fractional interval updates.

[0008] According to one embodiment of this application, the Gardner timing synchronization loop includes at least an interpolation filter, a timing error detection module, a second-order loop filter, and a numerically controlled oscillator.

[0009] According to one embodiment of this application, the initialization of the Gardner timing synchronization loop based on a digital phase-locked loop specifically includes: Initialize the parameters of the interpolation filter, timing error detection module, second-order loop filter, and numerically controlled oscillator, including initialization. The input signal for the interpolation filter is... This is the error detection value. For the input of the second-order loop filter, The output of the second-order loop filter, parameters of the numerically controlled oscillator. Decide to calculate the first The sampling points required for interpolation, and the numerically controlled oscillator. Decide to calculate the first The filter coefficients required for interpolation.

[0010] According to one embodiment of this application, the objective function is:

[0011] in, For the first j One frequency point; For the first j The actual filter frequency response at a given frequency point requires the filter tap coefficients to be solved. ; For the first j The ideal interpolation filter frequency response at each frequency point; For the first Linear weighting coefficients at each frequency point; P The total number of frequency points, the set of frequency points F By all composition.

[0012] According to one embodiment of this application, the step of establishing a linear constraint relationship based on the time-domain interpolation constraint of the interpolation filter specifically includes: Time-domain function of interpolation filter exist t =0 is 1, at time 1 At time 0, the time-domain function of the interpolation filter satisfies The linear constraint equations are obtained as follows:

[0013] in, These are the tap coefficients of the interpolation filter. Indicates the interpolation period. k Indicates the sampling time, i.e., the sampling period. k Interpolation points, For power-order basis functions, L This indicates the order of polynomial interpolation. N Indicates the filter length.

[0014] According to one embodiment of this application, the step of performing constrained optimization iteration under given signal bandwidth and image rejection frequency band conditions to solve for the optimal interpolation filter tap coefficients, so that the actual frequency domain response approximates the ideal frequency domain response, specifically includes: Based on the relationship between the objective function and linear constraints, the fminimax function from Matrix Laboratory is used. Pair of optimal interpolation filter tap coefficients on frequency domain point set Solve the problem.

[0015] According to one embodiment of this application, when adjusting the tap coefficients of the optimal interpolation filter... When solving, it is necessary to consider the set of frequency domain points. Iteration is required to obtain the optimal interpolation filter tap coefficients. .

[0016] According to one embodiment of this application, the step of implementing the optimal coefficients using a Farrow structure and embedding them into a Gardner timing synchronization loop to recover the optimal sampling time under the drive of fractional interval updates specifically includes: by m Selecting adjacent centers N The input sequence is composed of discrete sampled values. The obtained optimal interpolation filter coefficients are mapped to multi-branch sub-filter coefficients of a Farrow structure. Each sub-filter is then used to perform convolution operations on the input sequence to obtain polynomial coefficient terms, and these terms are then... μ We calculate the weighted sum of the independent variables over each term to obtain the interpolated output at the corresponding interpolation time, where... m Integer base points for interpolation. μ The decimal base point is the interpolation point.

[0017] According to a second aspect of the embodiments of this application, an electronic device is provided, comprising: At least one processor; and a memory communicatively connected to said at least one processor; The memory stores instructions that can be executed by the at least one processor, and the at least one processor executes the instructions stored in the memory to perform the method described in the first aspect.

[0018] According to a third aspect of the embodiments of this application, a computer-readable storage medium is provided for storing instructions that, when executed, cause the method described in the first aspect to be implemented.

[0019] Compared with existing technologies, the advantages of the above technical solution are as follows: This invention uses linear weighted minimum mean square error as the objective function, and combines the required signal bandwidth and image suppression bandwidth requirements to obtain optimized interpolation filter tap coefficients, making the actual frequency domain response closer to the ideal frequency domain response, thereby reducing interpolation errors and improving timing estimation accuracy. Simultaneously, the optimized coefficients are implemented using a Farrow structure and embedded in a Gardner loop, achieving optimal sampling time recovery under fractional interval update drive, balancing engineering implementation efficiency and synchronization accuracy. Compared with existing polynomial interpolation timing synchronization schemes using fixed coefficients, this invention can achieve optimizable design of the interpolation filter according to different experimental / transmission conditions, thereby improving the timing synchronization robustness and demodulation performance in high-speed data transmission scenarios. Attached Figure Description

[0020] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0021] Figure 1 This is a flowchart of the Gardner timing synchronization method based on an optimized interpolation filter, which is an embodiment of this application.

[0022] Figure 2 This is a communication system structure diagram of the Gardner timing synchronization method based on an optimized interpolation filter, according to an embodiment of this application.

[0023] Figure 3 The frequency response diagrams of different interpolation filters for Gardner timing synchronization are shown in the embodiments of this application.

[0024] Figure 4 The graph shows the bit error rate curves of different interpolation filters for Gardner timing synchronization in this application embodiment.

[0025] Figure 5 This is a schematic diagram of the structure of an electronic device according to an embodiment of this application. Detailed Implementation

[0026] The embodiments of this application are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar modules or modules having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application. Rather, the embodiments of this application include all variations, modifications, and equivalents falling within the spirit and scope of the appended claims.

[0027] To address the problems of fixed interpolation coefficients in traditional high-speed data transmission systems, difficulty in adapting to different experimental / transmission conditions, and insufficient timing synchronization accuracy under high-order modulation, this application proposes a Gardner timing synchronization method based on an optimized interpolation filter. It employs a classic digital phase-locked loop architecture for Gardner timing synchronization, using linear weighted minimum mean square error as the evaluation criterion. A linear constraint relationship is established based on the time-domain interpolation constraints of the interpolation filter. Combined with the required signal bandwidth and image suppression band, optimization iterations are performed under linear constraints to obtain the optimized interpolation filter coefficients. This makes the actual frequency domain response approximate the ideal frequency domain response, thereby improving the symbol timing estimation accuracy.

[0028] Please refer to Figure 1 The Gardner timing synchronization method based on optimized interpolation filters has the following specific steps: S100. Initialize the Gardner timing synchronization loop based on a digital phase-locked loop.

[0029] Please refer to Figure 2 In this embodiment, the Gardner timing synchronization loop includes at least an interpolation filter, a timing error detection module, a second-order loop filter, and a numerically controlled oscillator. During initialization, the parameters of the interpolation filter, timing error detection module, second-order loop filter, and numerically controlled oscillator need to be initialized. Specifically, this includes initializing the parameters of the interpolation filter, timing error detection module, second-order loop filter, and numerically controlled oscillator, including initializing... The input signal for the interpolation filter is... This is the error detection value. For the input of the second-order loop filter, The output of the second-order loop filter, parameters of the numerically controlled oscillator. Decide to calculate the first The sampling points required for interpolation, and the numerically controlled oscillator. Decide to calculate the first The filter coefficients required for interpolation.

[0030] S200. Using the linear weighted minimum mean square error as the objective function, establish a linear constraint relationship based on the time-domain interpolation constraint of the interpolation filter. Under the given signal bandwidth and image suppression frequency band, perform constraint optimization iteration to solve for the optimal interpolation filter tap coefficients, so that the actual frequency domain response approximates the ideal frequency domain response.

[0031] In this embodiment, the objective function is the linearly weighted minimum mean square error, which aims to make the actual frequency domain response approximate the ideal frequency domain response. The objective function is designed as follows:

[0032] in, For the first j One frequency point; For the first j The actual filter frequency response at a given frequency point requires the filter tap coefficients to be solved. ; For the first j The ideal interpolation filter frequency response at each frequency point; For the first Linear weighting coefficients at each frequency point; P The total number of frequency points, the set of frequency points F By all composition.

[0033] Because the time-domain function of the interpolation filter exist t =0 is 1, at time 1 At time 0, the time-domain function of the interpolation filter satisfies The linear constraint equations are obtained as follows:

[0034] in, These are the tap coefficients of the interpolation filter. Indicates the interpolation period. k Indicates the sampling time, i.e., the sampling period. k Interpolation points, L This indicates the order of polynomial interpolation. N Indicates the filter length. The basis functions are power-law functions, as follows:

[0035] Next, based on the relationship between the objective function and linear constraints, the fminimax function from Matrix Laboratory is used. Pair of optimal interpolation filter tap coefficients on frequency domain point set Solve the problem.

[0036] In this embodiment, the optimization coefficient is defined. The precision is 0.0001, and the initialization vector is... The function returns two results: one is the optimal coefficient vector obtained from solving the current set of frequency domain points. One is the minimum value of the current frequency domain point set obtained according to the objective function. This refers to the approximation of the current frequency domain function to the ideal frequency domain function. Since the frequency domain point set is randomly selected, solving for the frequency domain point set once will not yield the optimal value. Therefore, the frequency domain point set... Iteration is required to finally obtain the optimal interpolation filter tap coefficients. It satisfies the requirement that the actual frequency response is closest to the ideal frequency domain response.

[0037] S300. The optimal coefficients are implemented using a Farrow structure and embedded into the Gardner timing synchronization loop to complete the recovery of the optimal sampling time under the drive of fractional interval updates.

[0038] In this embodiment, m Selecting adjacent centers N (The filter length is N symbol periods, therefore selected) m Then, N / 2 sampling points are selected before and after, forming N) discrete sample values ​​to constitute the input sequence. The obtained optimal interpolation filter coefficients are mapped to the multi-branch sub-filter coefficients of the Farrow structure. Each sub-filter is then used to perform convolution operations on the input sequence to obtain polynomial coefficient terms, and... μ We calculate the weighted sum of the independent variables over each term to obtain the interpolated output at the corresponding interpolation time. m Integer base points for interpolation. μ This is the decimal base point for the interpolation point. For example, to interpolate a value at 2.4 in the middle of 1234, then m=2. μ =0.4, when the first symbol arrives, m=0, u=0; for each subsequent symbol, m = m+1, and jump to the next reference point. In this embodiment, m and u are collective terms. , These represent the integer and decimal positions of the k-th interpolation point, respectively. In the Gardner timing synchronization method, the previous interpolation point undergoes error detection, loop filtering, and numerical control oscillation before the next... , It is constantly being adjusted.

[0039] To verify the effectiveness of this invention, a detailed explanation is provided below with reference to simulation examples.

[0040] The simulation object is a medium-high orbit satellite with an altitude of 18,000 km. 16APSK modulation is currently the modulation method with the highest communication quality and transmission efficiency among multi-amplitude multi-phase modulation methods for satellite communication signals; therefore, 16APSK modulation is used in the simulation. Both the upsampling and downsampling rates are 8x, and both the shaping filter and the matched filter are raised cosine roll-off filters with a length of 64 bits and a roll-off factor of 0.25.

[0041] Please refer to Figure 3 The frequency response diagrams for different interpolation filters used in the Gardner timing synchronization simulation are presented. Please refer to [the documentation / reference]. Figure 4 The figure shows the bit error rate curves of different interpolation filters for Gardner timing synchronization during simulation. Among them, the bit error rate curves of different interpolation filters for Gardner timing synchronization are presented. Figure 3 It can be seen that the optimized four-point third-order and four-point second-order interpolation filters can form a steeper transition band in the frequency domain, and can better suppress the image frequency components that interfere with the baseband signal compared to the piecewise parabolic interpolation filter and the cubic interpolation filter. Meanwhile, the optimized four-point second-order interpolation filter has passband flatness comparable to the piecewise parabolic interpolation filter and the cubic interpolation filter. In practical applications, it can ensure relatively uniform signal processing within the passband, without causing large fluctuations in the signal's frequency response within the passband due to its own filtering characteristics. Furthermore, in terms of stopband attenuation, the optimized four-point second-order interpolation filter, compared to the piecewise parabolic interpolation filter, can utilize its own filtering characteristics to form faster attenuation in the high-frequency range, more efficiently filtering out unwanted high-frequency noise and interference, while its stopband attenuation performance is worse than that of the cubic interpolation filter. Finally, as shown in the figure, the optimized four-point third-order interpolation filter has the best performance in image frequency suppression, stopband attenuation, and passband flatness. Figure 4 In the results, with a roll-off factor of 0.25 and a bit error rate of 0.012, the optimized four-point third-order interpolation filter improves performance by 1 dB compared to the four-point second-order interpolation, by approximately 3 dB compared to cubic interpolation, and by approximately 5 dB compared to piecewise parabolic interpolation. This demonstrates that the improved interpolation method can enhance the accuracy of symbol decision and reduce the bit error rate. Furthermore, the performance advantages of the optimized interpolation filter proposed in this invention become even more pronounced as the roll-off factor decreases.

[0042] Based on the same technical concept, embodiments of this application also provide an electronic device that can implement the Gardner timing synchronization method based on an optimized interpolation filter provided in the above embodiments of the present invention. In one embodiment, the electronic device can be a server, a terminal device, or other electronic devices. Figure 5 As shown, the electronic device may include: At least one processor and a memory connected to the at least one processor. In this embodiment of the invention, the specific connection medium between the processor and the memory is not limited. Figure 5 The example used is the connection between the processor and memory via a bus. The bus... Figure 5 The connections between other components are indicated by thick lines and are for illustrative purposes only, not as limiting information. Buses can be divided into address buses, data buses, control buses, etc., but for ease of representation, [the specific bus type is not shown here]. Figure 5 The processor is represented by a single thick line, but this does not imply that there is only one bus or one type of bus. Alternatively, a processor can also be called a controller; there are no restrictions on the name.

[0043] In this embodiment of the invention, the memory stores instructions executable by at least one processor. By executing the instructions stored in the memory, the at least one processor can perform the Gardner timing synchronization method based on an optimized interpolation filter, as described above. The processor can implement... Figure 5 The functions of each module in the device shown.

[0044] The processor is the control center of the device. It can connect to various parts of the control device through various interfaces and lines. By running or executing instructions stored in memory and calling data stored in memory, it can monitor the device's various functions and process data, thereby enabling overall monitoring of the device.

[0045] In an alternative design, the processor may include one or more processing units. The processor may integrate an application processor and a modem processor, wherein the application processor primarily handles the operating system, user interface, and applications, while the modem processor primarily handles wireless communication. It is understood that the modem processor may also not be integrated into the processor. In some embodiments, the processor and memory may be implemented on the same chip; in some embodiments, they may also be implemented separately on separate chips.

[0046] The processor can be a general-purpose processor, such as a CPU, digital signal processor, application-specific integrated circuit, field-programmable array, or other programmable logic device, discrete gate or transistor logic device, or discrete hardware component, capable of implementing or executing the methods, steps, and logic block diagrams disclosed in the embodiments of this invention. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the Gardner timing synchronization method based on an optimized interpolation filter disclosed in the embodiments of this invention can be directly manifested as execution by a hardware processor, or as execution by a combination of hardware and software modules within the processor.

[0047] Memory, as a non-volatile computer-readable storage medium, can be used to store non-volatile software programs, non-volatile computer-executable programs, and modules. Memory can include at least one type of storage medium, such as flash memory, hard disk, multimedia card, card-type memory, random access memory (RAM), static random access memory (SRAM), programmable read-only memory (PROM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), magnetic memory, magnetic disk, optical disk, etc. Memory is any other medium capable of carrying or storing desired program code in the form of instructions or data structures, and accessible by a computer, but is not limited thereto. In embodiments of the present invention, memory can also be a circuit or any other device capable of implementing storage functions, used to store program instructions and / or data.

[0048] By designing and programming the processor, the code corresponding to the Gardner timing synchronization method based on the optimized interpolation filter described in the foregoing embodiments can be embedded into the chip, enabling the chip to execute the steps of the method described in the foregoing embodiments during runtime. How to design and program a processor is a technique well-known to those skilled in the art, and will not be elaborated upon here.

[0049] Based on the same inventive concept, embodiments of the present invention also provide a storage medium storing computer instructions that, when executed on a computer, cause the computer to perform a Gardner timing synchronization method based on an optimized interpolation filter as described above.

[0050] In some alternative embodiments, the present invention also provides that various aspects of the Gardner timing synchronization method based on an optimized interpolation filter can also be implemented as a program product comprising program code that, when the program product is run on a device, causes the control device to perform the steps in the Gardner timing synchronization method based on an optimized interpolation filter according to various exemplary embodiments of the present invention as described in this specification.

[0051] It should be noted that although several units or sub-units of the apparatus have been mentioned in the detailed description above, this division is merely exemplary and not mandatory. In fact, according to embodiments of the invention, the features and functions of two or more units described above can be embodied in one unit. Conversely, the features and functions of one unit described above can be further divided and embodied by multiple units. Furthermore, although the operation of the method of the invention is described in a specific order in the drawings, this does not require or imply that these operations must be performed in that specific order, or that all the operations shown must be performed to achieve the desired result. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into one step, and / or one step may be broken down into multiple steps.

[0052] 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.

[0053] 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 server, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0054] Program code for performing the operations of this invention can be written using any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, as well as conventional procedural programming languages ​​such as C or similar languages. The program code can be executed entirely on the user's computing device, partially on the user's device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server.

[0055] In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0056] 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.

[0057] 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.

[0058] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A Gardner timing synchronization method based on an optimized interpolation filter, characterized in that, include: Initialize the Gardner timing synchronization loop based on a digital phase-locked loop; Using the linear weighted minimum mean square error as the objective function, a linear constraint relationship is established based on the time-domain interpolation constraint of the interpolation filter. Under the given signal bandwidth and image suppression frequency band, constraint optimization iteration is performed to solve for the optimal interpolation filter tap coefficients, so that the actual frequency domain response approximates the ideal frequency domain response. The optimal coefficients are implemented using a Farrow structure and embedded in the Gardner timing synchronization loop, and the optimal sampling time is recovered under the drive of fractional interval updates.

2. The Gardner timing synchronization method based on an optimized interpolation filter according to claim 1, characterized in that, The Gardner timing synchronization loop includes at least an interpolation filter, a timing error detection module, a second-order loop filter, and a numerically controlled oscillator.

3. The Gardner timing synchronization method based on an optimized interpolation filter according to claim 2, characterized in that, The initialization of the Gardner timing synchronization loop based on a digital phase-locked loop specifically includes: Initialize the parameters of the interpolation filter, timing error detection module, second-order loop filter, and numerically controlled oscillator, including initialization. The input signal for the interpolation filter is... This is the error detection value. For the input of the second-order loop filter, The output of the second-order loop filter, parameters of the numerically controlled oscillator. Decide to calculate the first The sampling points required for interpolation, and the numerically controlled oscillator. Decide to calculate the first The filter coefficients required for interpolation.

4. The Gardner timing synchronization method based on an optimized interpolation filter according to claim 3, characterized in that, The objective function is: in, For the first j One frequency point; For the first j The actual filter frequency response at a given frequency point requires the filter tap coefficients to be solved. ; For the first j The ideal interpolation filter frequency response at each frequency point; For the first Linear weighting coefficients at each frequency point; P The total number of frequency points, the set of frequency points F By all composition.

5. The Gardner timing synchronization method based on an optimized interpolation filter according to claim 3 or 4, characterized in that, The establishment of linear constraint relationships based on the time-domain interpolation constraints of the interpolation filter specifically includes: Time-domain function of interpolation filter exist t =0 is 1, at time 1 At time 0, the time-domain function of the interpolation filter satisfies The linear constraint equations are obtained as follows: in, These are the tap coefficients of the interpolation filter. Indicates the interpolation period. k Indicates the sampling time, i.e., the sampling period. k Interpolation points, For power-order basis functions, L This indicates the order of polynomial interpolation. N Indicates the filter length.

6. The Gardner timing synchronization method based on an optimized interpolation filter according to claim 5, characterized in that, The process of constrained optimization iteration under given signal bandwidth and image rejection frequency band conditions to solve for the optimal interpolation filter tap coefficients, so that the actual frequency domain response approximates the ideal frequency domain response, specifically includes: Based on the relationship between the objective function and linear constraints, the fminimax function from Matrix Laboratory is used. Pair of optimal interpolation filter tap coefficients on frequency domain point set Solve the problem.

7. The Gardner timing synchronization method based on an optimized interpolation filter according to claim 6, characterized in that, The optimal interpolation filter tap coefficients When solving, it is necessary to consider the set of frequency domain points. Iteration is required to obtain the optimal interpolation filter tap coefficients. .

8. The Gardner timing synchronization method based on an optimized interpolation filter according to claim 1, characterized in that, The process of implementing the optimal coefficients using a Farrow structure and embedding them into the Gardner timing synchronization loop, and restoring the optimal sampling time under the drive of fractional interval updates, specifically includes: by m Selecting adjacent centers N The input sequence is composed of discrete sampled values. The obtained optimal interpolation filter coefficients are mapped to multi-branch sub-filter coefficients of a Farrow structure. Each sub-filter is then used to perform convolution operations on the input sequence to obtain polynomial coefficient terms, and these terms are then... μ We calculate the weighted sum of the independent variables over each term to obtain the interpolated output at the corresponding interpolation time, where... m Integer base points for interpolation. μ The decimal base point is the interpolation point.

9. An electronic device, characterized in that, include: At least one processor; and a memory communicatively connected to the at least one processor; The memory stores instructions executable by the at least one processor, which executes the instructions stored in the memory to perform the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium is used to store instructions that, when executed, cause the method as described in any one of claims 1 to 8 to be implemented.

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